Daily Papers

Conventional class-guided diffusion models generally succeed in generating images with correct semantic content, but often struggle with texture details. This limitation stems from the usage of class priors, which only provide coarse and limited conditional information. To address this issue, we propose Diffusion on Diffusion (DoD), an innovative multi-stage generation framework that first extracts visual priors from previously generated samples, then provides rich guidance for the diffusion model leveraging visual priors from the early stages of diffusion sampling. Specifically, we introduce a latent embedding module that employs a compression-reconstruction approach to discard redundant detail information from the conditional samples in each stage, retaining only the semantic information for guidance. We evaluate DoD on the popular ImageNet-256 times 256 dataset, reducing 7times training cost compared to SiT and DiT with even better performance in terms of the FID-50K score. Our largest model DoD-XL achieves an FID-50K score of 1.83 with only 1 million training steps, which surpasses other state-of-the-art methods without bells and whistles during inference.

Current diffusion-based image restoration methods feed degraded input images as conditions into the noise estimation network. However, interpreting this diffusion process is challenging since it essentially generates the target image from the noise. To establish a unified and more interpretable model for image generation and restoration, we propose residual denoising diffusion models (RDDM). In contrast to existing diffusion models (e.g., DDPM or DDIM) that focus solely on noise estimation, our RDDM predicts residuals to represent directional diffusion from the target domain to the input domain, while concurrently estimating noise to account for random perturbations in the diffusion process. The introduction of residuals allows us to redefine the forward diffusion process, wherein the target image progressively diffuses into a purely noisy image or a noise-carrying input image, thus unifying image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation, and propose a partially path-independent generation process to better understand the reverse process. Notably, with native support for conditional inputs, our RDDM enables a generic UNet, trained with only an ell _1 loss and a batch size of 1, to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration, application, and development of our innovative framework (https://github.com/nachifur/RDDM).

Discrete diffusion has achieved state-of-the-art performance, outperforming or approaching autoregressive models on standard benchmarks. In this work, we introduce Discrete Diffusion with Planned Denoising (DDPD), a novel framework that separates the generation process into two models: a planner and a denoiser. At inference time, the planner selects which positions to denoise next by identifying the most corrupted positions in need of denoising, including both initially corrupted and those requiring additional refinement. This plan-and-denoise approach enables more efficient reconstruction during generation by iteratively identifying and denoising corruptions in the optimal order. DDPD outperforms traditional denoiser-only mask diffusion methods, achieving superior results on language modeling benchmarks such as text8, OpenWebText, and token-based generation on ImageNet 256 times 256. Notably, in language modeling, DDPD significantly reduces the performance gap between diffusion-based and autoregressive methods in terms of generative perplexity. Code is available at https://github.com/liusulin/DDPD.

Denoising diffusion models hold great promise for generating diverse and realistic human motions. However, existing motion diffusion models largely disregard the laws of physics in the diffusion process and often generate physically-implausible motions with pronounced artifacts such as floating, foot sliding, and ground penetration. This seriously impacts the quality of generated motions and limits their real-world application. To address this issue, we present a novel physics-guided motion diffusion model (PhysDiff), which incorporates physical constraints into the diffusion process. Specifically, we propose a physics-based motion projection module that uses motion imitation in a physics simulator to project the denoised motion of a diffusion step to a physically-plausible motion. The projected motion is further used in the next diffusion step to guide the denoising diffusion process. Intuitively, the use of physics in our model iteratively pulls the motion toward a physically-plausible space, which cannot be achieved by simple post-processing. Experiments on large-scale human motion datasets show that our approach achieves state-of-the-art motion quality and improves physical plausibility drastically (>78% for all datasets).

Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detection. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

In recent advancements in high-fidelity image generation, Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a key player. However, their application at high resolutions presents significant computational challenges. Current methods, such as patchifying, expedite processes in UNet and Transformer architectures but at the expense of representational capacity. Addressing this, we introduce the Diffusion State Space Model (DiffuSSM), an architecture that supplants attention mechanisms with a more scalable state space model backbone. This approach effectively handles higher resolutions without resorting to global compression, thus preserving detailed image representation throughout the diffusion process. Our focus on FLOP-efficient architectures in diffusion training marks a significant step forward. Comprehensive evaluations on both ImageNet and LSUN datasets at two resolutions demonstrate that DiffuSSMs are on par or even outperform existing diffusion models with attention modules in FID and Inception Score metrics while significantly reducing total FLOP usage.

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In this paper, we establish the interpretation of DDMs in terms of image restoration (IR). Integrating IR literature allows us to use an alternative objective and diverse forward processes, not confining to the diffusion process. By imposing prior knowledge on the loss function grounded on MAP-based estimation, we eliminate the need for the expensive sampling of DDMs. Also, we propose a multi-scale training, which improves the performance compared to the diffusion process, by taking advantage of the flexibility of the forward process. Experimental results demonstrate that our model improves the quality and efficiency of both training and inference. Furthermore, we show the applicability of our model to inverse problems. We believe that our framework paves the way for designing a new type of flexible general generative model.

Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single continuous Gaussian distribution arguably represents an unnecessarily challenging learning problem. We propose Discrete-Continuous Latent Variable Diffusion Models (DisCo-Diff) to simplify this task by introducing complementary discrete latent variables. We augment DMs with learnable discrete latents, inferred with an encoder, and train DM and encoder end-to-end. DisCo-Diff does not rely on pre-trained networks, making the framework universally applicable. The discrete latents significantly simplify learning the DM's complex noise-to-data mapping by reducing the curvature of the DM's generative ODE. An additional autoregressive transformer models the distribution of the discrete latents, a simple step because DisCo-Diff requires only few discrete variables with small codebooks. We validate DisCo-Diff on toy data, several image synthesis tasks as well as molecular docking, and find that introducing discrete latents consistently improves model performance. For example, DisCo-Diff achieves state-of-the-art FID scores on class-conditioned ImageNet-64/128 datasets with ODE sampler.

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples that are highly diverse and representative of the underlying distribution. However, one of the main limitations of diffusion models is the complexity of sample generation, since a large number of inference timesteps is required to faithfully capture the data distribution. In this paper, we present MMD-DDM, a novel method for fast sampling of diffusion models. Our approach is based on the idea of using the Maximum Mean Discrepancy (MMD) to finetune the learned distribution with a given budget of timesteps. This allows the finetuned model to significantly improve the speed-quality trade-off, by substantially increasing fidelity in inference regimes with few steps or, equivalently, by reducing the required number of steps to reach a target fidelity, thus paving the way for a more practical adoption of diffusion models in a wide range of applications. We evaluate our approach on unconditional image generation with extensive experiments across the CIFAR-10, CelebA, ImageNet and LSUN-Church datasets. Our findings show that the proposed method is able to produce high-quality samples in a fraction of the time required by widely-used diffusion models, and outperforms state-of-the-art techniques for accelerated sampling. Code is available at: https://github.com/diegovalsesia/MMD-DDM.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

A dramatic influx of diffusion-generated images has marked recent years, posing unique challenges to current detection technologies. While the task of identifying these images falls under binary classification, a seemingly straightforward category, the computational load is significant when employing the "reconstruction then compare" technique. This approach, known as DIRE (Diffusion Reconstruction Error), not only identifies diffusion-generated images but also detects those produced by GANs, highlighting the technique's broad applicability. To address the computational challenges and improve efficiency, we propose distilling the knowledge embedded in diffusion models to develop rapid deepfake detection models. Our approach, aimed at creating a small, fast, cheap, and lightweight diffusion synthesized deepfake detector, maintains robust performance while significantly reducing operational demands. Maintaining performance, our experimental results indicate an inference speed 3.2 times faster than the existing DIRE framework. This advance not only enhances the practicality of deploying these systems in real-world settings but also paves the way for future research endeavors that seek to leverage diffusion model knowledge.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.

Test-time adaptation harnesses test inputs to improve the accuracy of a model trained on source data when tested on shifted target data. Existing methods update the source model by (re-)training on each target domain. While effective, re-training is sensitive to the amount and order of the data and the hyperparameters for optimization. We instead update the target data, by projecting all test inputs toward the source domain with a generative diffusion model. Our diffusion-driven adaptation method, DDA, shares its models for classification and generation across all domains. Both models are trained on the source domain, then fixed during testing. We augment diffusion with image guidance and self-ensembling to automatically decide how much to adapt. Input adaptation by DDA is more robust than prior model adaptation approaches across a variety of corruptions, architectures, and data regimes on the ImageNet-C benchmark. With its input-wise updates, DDA succeeds where model adaptation degrades on too little data in small batches, dependent data in non-uniform order, or mixed data with multiple corruptions.

Denoising diffusion models have emerged as the go-to framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution (OOD) tasks, which remains an under-explored challenge. Realistic reconstructions inconsistent with the measured data can be generated, hallucinating image features that are uniquely present in the training dataset. To simultaneously enforce data-consistency and leverage data-driven priors, we introduce a novel sampling framework called Steerable Conditional Diffusion. This framework adapts the denoising network specifically to the available measured data. Utilising our proposed method, we achieve substantial enhancements in OOD performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by building a diffusion process, directly bridging the clean and the corrupted for specific inverse problems. In this paper, we first unify these existing works under the name Direct Diffusion Bridges (DDB), showing that while motivated by different theories, the resulting algorithms only differ in the choice of parameters. Then, we highlight a critical limitation of the current DDB framework, namely that it does not ensure data consistency. To address this problem, we propose a modified inference procedure that imposes data consistency without the need for fine-tuning. We term the resulting method data Consistent DDB (CDDB), which outperforms its inconsistent counterpart in terms of both perception and distortion metrics, thereby effectively pushing the Pareto-frontier toward the optimum. Our proposed method achieves state-of-the-art results on both evaluation criteria, showcasing its superiority over existing methods.

Diffusion model-based approaches have shown promise in data-driven planning, but there are no safety guarantees, thus making it hard to be applied for safety-critical applications. To address these challenges, we propose a new method, called SafeDiffuser, to ensure diffusion probabilistic models satisfy specifications by using a class of control barrier functions. The key idea of our approach is to embed the proposed finite-time diffusion invariance into the denoising diffusion procedure, which enables trustworthy diffusion data generation. Moreover, we demonstrate that our finite-time diffusion invariance method through generative models not only maintains generalization performance but also creates robustness in safe data generation. We test our method on a series of safe planning tasks, including maze path generation, legged robot locomotion, and 3D space manipulation, with results showing the advantages of robustness and guarantees over vanilla diffusion models.

Diffusion models have achieved remarkable success in the domain of text-guided image generation and, more recently, in text-guided image editing. A commonly adopted strategy for editing real images involves inverting the diffusion process to obtain a noisy representation of the original image, which is then denoised to achieve the desired edits. However, current methods for diffusion inversion often struggle to produce edits that are both faithful to the specified text prompt and closely resemble the source image. To overcome these limitations, we introduce a novel and adaptable diffusion inversion technique for real image editing, which is grounded in a theoretical analysis of the role of eta in the DDIM sampling equation for enhanced editability. By designing a universal diffusion inversion method with a time- and region-dependent eta function, we enable flexible control over the editing extent. Through a comprehensive series of quantitative and qualitative assessments, involving a comparison with a broad array of recent methods, we demonstrate the superiority of our approach. Our method not only sets a new benchmark in the field but also significantly outperforms existing strategies.

Denoising diffusion (score-based) generative models have recently achieved significant accomplishments in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data into noise and a backward denoising process for sampling data from noise. Unfortunately, the generation process of current denoising diffusion models is notoriously slow due to the lengthy iterative noise estimations, which rely on cumbersome neural networks. It prevents the diffusion models from being widely deployed, especially on edge devices. Previous works accelerate the generation process of diffusion model (DM) via finding shorter yet effective sampling trajectories. However, they overlook the cost of noise estimation with a heavy network in every iteration. In this work, we accelerate generation from the perspective of compressing the noise estimation network. Due to the difficulty of retraining DMs, we exclude mainstream training-aware compression paradigms and introduce post-training quantization (PTQ) into DM acceleration. However, the output distributions of noise estimation networks change with time-step, making previous PTQ methods fail in DMs since they are designed for single-time step scenarios. To devise a DM-specific PTQ method, we explore PTQ on DM in three aspects: quantized operations, calibration dataset, and calibration metric. We summarize and use several observations derived from all-inclusive investigations to formulate our method, which especially targets the unique multi-time-step structure of DMs. Experimentally, our method can directly quantize full-precision DMs into 8-bit models while maintaining or even improving their performance in a training-free manner. Importantly, our method can serve as a plug-and-play module on other fast-sampling methods, e.g., DDIM. The code is available at https://github.com/42Shawn/PTQ4DM .

Denoising diffusion models (DDMs) have led to staggering performance leaps in image generation, editing and restoration. However, existing DDMs use very large datasets for training. Here, we introduce a framework for training a DDM on a single image. Our method, which we coin SinDDM, learns the internal statistics of the training image by using a multi-scale diffusion process. To drive the reverse diffusion process, we use a fully-convolutional light-weight denoiser, which is conditioned on both the noise level and the scale. This architecture allows generating samples of arbitrary dimensions, in a coarse-to-fine manner. As we illustrate, SinDDM generates diverse high-quality samples, and is applicable in a wide array of tasks, including style transfer and harmonization. Furthermore, it can be easily guided by external supervision. Particularly, we demonstrate text-guided generation from a single image using a pre-trained CLIP model.

Denoising diffusion models (DDMs) have attracted attention for their exceptional generation quality and diversity. This success is largely attributed to the use of class- or text-conditional diffusion guidance methods, such as classifier and classifier-free guidance. In this paper, we present a more comprehensive perspective that goes beyond the traditional guidance methods. From this generalized perspective, we introduce novel condition- and training-free strategies to enhance the quality of generated images. As a simple solution, blur guidance improves the suitability of intermediate samples for their fine-scale information and structures, enabling diffusion models to generate higher quality samples with a moderate guidance scale. Improving upon this, Self-Attention Guidance (SAG) uses the intermediate self-attention maps of diffusion models to enhance their stability and efficacy. Specifically, SAG adversarially blurs only the regions that diffusion models attend to at each iteration and guides them accordingly. Our experimental results show that our SAG improves the performance of various diffusion models, including ADM, IDDPM, Stable Diffusion, and DiT. Moreover, combining SAG with conventional guidance methods leads to further improvement.

We introduce the Joint Video-Image Diffusion model (JVID), a novel approach to generating high-quality and temporally coherent videos. We achieve this by integrating two diffusion models: a Latent Image Diffusion Model (LIDM) trained on images and a Latent Video Diffusion Model (LVDM) trained on video data. Our method combines these models in the reverse diffusion process, where the LIDM enhances image quality and the LVDM ensures temporal consistency. This unique combination allows us to effectively handle the complex spatio-temporal dynamics in video generation. Our results demonstrate quantitative and qualitative improvements in producing realistic and coherent videos.

Unsupervised out-of-distribution detection (OOD) seeks to identify out-of-domain data by learning only from unlabeled in-domain data. We present a novel approach for this task - Lift, Map, Detect (LMD) - that leverages recent advancement in diffusion models. Diffusion models are one type of generative models. At their core, they learn an iterative denoising process that gradually maps a noisy image closer to their training manifolds. LMD leverages this intuition for OOD detection. Specifically, LMD lifts an image off its original manifold by corrupting it, and maps it towards the in-domain manifold with a diffusion model. For an out-of-domain image, the mapped image would have a large distance away from its original manifold, and LMD would identify it as OOD accordingly. We show through extensive experiments that LMD achieves competitive performance across a broad variety of datasets.

Finding an initial noise vector that produces an input image when fed into the diffusion process (known as inversion) is an important problem in denoising diffusion models (DDMs), with applications for real image editing. The state-of-the-art approach for real image editing with inversion uses denoising diffusion implicit models (DDIMs) to deterministically noise the image to the intermediate state along the path that the denoising would follow given the original conditioning. However, DDIM inversion for real images is unstable as it relies on local linearization assumptions, which result in the propagation of errors, leading to incorrect image reconstruction and loss of content. To alleviate these problems, we propose Exact Diffusion Inversion via Coupled Transformations (EDICT), an inversion method that draws inspiration from affine coupling layers. EDICT enables mathematically exact inversion of real and model-generated images by maintaining two coupled noise vectors which are used to invert each other in an alternating fashion. Using Stable Diffusion, a state-of-the-art latent diffusion model, we demonstrate that EDICT successfully reconstructs real images with high fidelity. On complex image datasets like MS-COCO, EDICT reconstruction significantly outperforms DDIM, improving the mean square error of reconstruction by a factor of two. Using noise vectors inverted from real images, EDICT enables a wide range of image edits--from local and global semantic edits to image stylization--while maintaining fidelity to the original image structure. EDICT requires no model training/finetuning, prompt tuning, or extra data and can be combined with any pretrained DDM. Code is available at https://github.com/salesforce/EDICT.

Diffusion model (DM) has achieved SOTA performance by modeling the image synthesis process into a sequential application of a denoising network. However, different from image synthesis, image restoration (IR) has a strong constraint to generate results in accordance with ground-truth. Thus, for IR, traditional DMs running massive iterations on a large model to estimate whole images or feature maps is inefficient. To address this issue, we propose an efficient DM for IR (DiffIR), which consists of a compact IR prior extraction network (CPEN), dynamic IR transformer (DIRformer), and denoising network. Specifically, DiffIR has two training stages: pretraining and training DM. In pretraining, we input ground-truth images into CPEN_{S1} to capture a compact IR prior representation (IPR) to guide DIRformer. In the second stage, we train the DM to directly estimate the same IRP as pretrained CPEN_{S1} only using LQ images. We observe that since the IPR is only a compact vector, DiffIR can use fewer iterations than traditional DM to obtain accurate estimations and generate more stable and realistic results. Since the iterations are few, our DiffIR can adopt a joint optimization of CPEN_{S2}, DIRformer, and denoising network, which can further reduce the estimation error influence. We conduct extensive experiments on several IR tasks and achieve SOTA performance while consuming less computational costs. Code is available at https://github.com/Zj-BinXia/DiffIR.

Distillation techniques have substantially improved the sampling speed of diffusion models, allowing of the generation within only one step or a few steps. However, these distillation methods require extensive training for each dataset, sampler, and network, which limits their practical applicability. To address this limitation, we propose a straightforward distillation approach, Distilled-ODE solvers (D-ODE solvers), that optimizes the ODE solver rather than training the denoising network. D-ODE solvers are formulated by simply applying a single parameter adjustment to existing ODE solvers. Subsequently, D-ODE solvers with smaller steps are optimized by ODE solvers with larger steps through distillation over a batch of samples. Our comprehensive experiments indicate that D-ODE solvers outperform existing ODE solvers, including DDIM, PNDM, DPM-Solver, DEIS, and EDM, especially when generating samples with fewer steps. Our method incur negligible computational overhead compared to previous distillation techniques, enabling simple and rapid integration with previous samplers. Qualitative analysis further shows that D-ODE solvers enhance image quality while preserving the sampling trajectory of ODE solvers.

Latent diffusion models are the state-of-the-art for synthetic image generation. To align these models with human preferences, training the models using reinforcement learning on human feedback is crucial. Black et. al 2024 introduced denoising diffusion policy optimisation (DDPO), which accounts for the iterative denoising nature of the generation by modelling it as a Markov chain with a final reward. As the reward is a single value that determines the model's performance on the entire image, the model has to navigate a very sparse reward landscape and so requires a large sample count. In this work, we extend the DDPO by presenting the Pixel-wise Policy Optimisation (PXPO) algorithm, which can take feedback for each pixel, providing a more nuanced reward to the model.

While 2D diffusion models generate realistic, high-detail images, 3D shape generation methods like Score Distillation Sampling (SDS) built on these 2D diffusion models produce cartoon-like, over-smoothed shapes. To help explain this discrepancy, we show that the image guidance used in Score Distillation can be understood as the velocity field of a 2D denoising generative process, up to the choice of a noise term. In particular, after a change of variables, SDS resembles a high-variance version of Denoising Diffusion Implicit Models (DDIM) with a differently-sampled noise term: SDS introduces noise i.i.d. randomly at each step, while DDIM infers it from the previous noise predictions. This excessive variance can lead to over-smoothing and unrealistic outputs. We show that a better noise approximation can be recovered by inverting DDIM in each SDS update step. This modification makes SDS's generative process for 2D images almost identical to DDIM. In 3D, it removes over-smoothing, preserves higher-frequency detail, and brings the generation quality closer to that of 2D samplers. Experimentally, our method achieves better or similar 3D generation quality compared to other state-of-the-art Score Distillation methods, all without training additional neural networks or multi-view supervision, and providing useful insights into relationship between 2D and 3D asset generation with diffusion models.

Video generation using diffusion-based models is constrained by high computational costs due to the frame-wise iterative diffusion process. This work presents a Diffusion Reuse MOtion (Dr. Mo) network to accelerate latent video generation. Our key discovery is that coarse-grained noises in earlier denoising steps have demonstrated high motion consistency across consecutive video frames. Following this observation, Dr. Mo propagates those coarse-grained noises onto the next frame by incorporating carefully designed, lightweight inter-frame motions, eliminating massive computational redundancy in frame-wise diffusion models. The more sensitive and fine-grained noises are still acquired via later denoising steps, which can be essential to retain visual qualities. As such, deciding which intermediate steps should switch from motion-based propagations to denoising can be a crucial problem and a key tradeoff between efficiency and quality. Dr. Mo employs a meta-network named Denoising Step Selector (DSS) to dynamically determine desirable intermediate steps across video frames. Extensive evaluations on video generation and editing tasks have shown that Dr. Mo can substantially accelerate diffusion models in video tasks with improved visual qualities.

We introduce a method for generating realistic pedestrian trajectories and full-body animations that can be controlled to meet user-defined goals. We draw on recent advances in guided diffusion modeling to achieve test-time controllability of trajectories, which is normally only associated with rule-based systems. Our guided diffusion model allows users to constrain trajectories through target waypoints, speed, and specified social groups while accounting for the surrounding environment context. This trajectory diffusion model is integrated with a novel physics-based humanoid controller to form a closed-loop, full-body pedestrian animation system capable of placing large crowds in a simulated environment with varying terrains. We further propose utilizing the value function learned during RL training of the animation controller to guide diffusion to produce trajectories better suited for particular scenarios such as collision avoidance and traversing uneven terrain. Video results are available on the project page at https://nv-tlabs.github.io/trace-pace .

Digital Surface Models (DSM) offer a wealth of height information for understanding the Earth's surface as well as monitoring the existence or change in natural and man-made structures. Classical height estimation requires multi-view geospatial imagery or LiDAR point clouds which can be expensive to acquire. Single-view height estimation using neural network based models shows promise however it can struggle with reconstructing high resolution features. The latest advancements in diffusion models for high resolution image synthesis and editing have yet to be utilized for remote sensing imagery, particularly height estimation. Our approach involves training a generative diffusion model to learn the joint distribution of optical and DSM images across both domains as a Markov chain. This is accomplished by minimizing a denoising score matching objective while being conditioned on the source image to generate realistic high resolution 3D surfaces. In this paper we experiment with conditional denoising diffusion probabilistic models (DDPM) for height estimation from a single remotely sensed image and show promising results on the Vaihingen benchmark dataset.

Building on recent advances in image generation, we present a fully data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising operations on top of a Gaussian noise distribution. We view the diffusion denoising process as a sequential decision making process, and show that it exhibits compounding errors similar to exposure bias issues in imitation learning problems. To mitigate these issues, we adapt the scheduled sampling algorithm to diffusion training. We conduct experiments on four markup datasets: mathematical formulas (LaTeX), table layouts (HTML), sheet music (LilyPond), and molecular images (SMILES). These experiments each verify the effectiveness of the diffusion process and the use of scheduled sampling to fix generation issues. These results also show that the markup-to-image task presents a useful controlled compositional setting for diagnosing and analyzing generative image models.

Applying pre-trained generative denoising diffusion models (DDMs) for downstream tasks such as image semantic editing usually requires either fine-tuning DDMs or learning auxiliary editing networks in the existing literature. In this work, we present our BoundaryDiffusion method for efficient, effective and light-weight semantic control with frozen pre-trained DDMs, without learning any extra networks. As one of the first learning-free diffusion editing works, we start by seeking a comprehensive understanding of the intermediate high-dimensional latent spaces by theoretically and empirically analyzing their probabilistic and geometric behaviors in the Markov chain. We then propose to further explore the critical step for editing in the denoising trajectory that characterizes the convergence of a pre-trained DDM and introduce an automatic search method. Last but not least, in contrast to the conventional understanding that DDMs have relatively poor semantic behaviors, we prove that the critical latent space we found already exhibits semantic subspace boundaries at the generic level in unconditional DDMs, which allows us to do controllable manipulation by guiding the denoising trajectory towards the targeted boundary via a single-step operation. We conduct extensive experiments on multiple DPMs architectures (DDPM, iDDPM) and datasets (CelebA, CelebA-HQ, LSUN-church, LSUN-bedroom, AFHQ-dog) with different resolutions (64, 256), achieving superior or state-of-the-art performance in various task scenarios (image semantic editing, text-based editing, unconditional semantic control) to demonstrate the effectiveness.

Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the intrinsic mutual interference among image regions contradicts the need for practical downstream application scenarios where the preservation of low-level pixel information from given conditioning is desired (e.g., customization tasks like personalized generation and inpainting based on a user-provided single image). In this work, we investigate the diffusion (physics) in diffusion (machine learning) properties and propose our Cyclic One-Way Diffusion (COW) method to control the direction of diffusion phenomenon given a pre-trained frozen diffusion model for versatile customization application scenarios, where the low-level pixel information from the conditioning needs to be preserved. Notably, unlike most current methods that incorporate additional conditions by fine-tuning the base text-to-image diffusion model or learning auxiliary networks, our method provides a novel perspective to understand the task needs and is applicable to a wider range of customization scenarios in a learning-free manner. Extensive experiment results show that our proposed COW can achieve more flexible customization based on strict visual conditions in different application settings. Project page: https://wangruoyu02.github.io/cow.github.io/.

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at https://github.com/mandt-lab/PSLD.

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Denoising Diffusion Probabilistic Models (DDPMs) have garnered popularity for data generation across various domains. However, a significant bottleneck is the necessity for whole-network computation during every step of the generative process, leading to high computational overheads. This paper presents a novel framework, Denoising Diffusion Step-aware Models (DDSM), to address this challenge. Unlike conventional approaches, DDSM employs a spectrum of neural networks whose sizes are adapted according to the importance of each generative step, as determined through evolutionary search. This step-wise network variation effectively circumvents redundant computational efforts, particularly in less critical steps, thereby enhancing the efficiency of the diffusion model. Furthermore, the step-aware design can be seamlessly integrated with other efficiency-geared diffusion models such as DDIMs and latent diffusion, thus broadening the scope of computational savings. Empirical evaluations demonstrate that DDSM achieves computational savings of 49% for CIFAR-10, 61% for CelebA-HQ, 59% for LSUN-bedroom, 71% for AFHQ, and 76% for ImageNet, all without compromising the generation quality. Our code and models will be publicly available.

Diffusion models have recently exhibited remarkable performance on synthetic data. After a diffusion path is selected, a base model, such as UNet, operates as a denoising autoencoder, primarily predicting noises that need to be eliminated step by step. Consequently, it is crucial to employ a model that aligns with the expected budgets to facilitate superior synthetic performance. In this paper, we meticulously analyze the diffusion model and engineer a base model search approach, denoted "DiffNAS". Specifically, we leverage GPT-4 as a supernet to expedite the search, supplemented with a search memory to enhance the results. Moreover, we employ RFID as a proxy to promptly rank the experimental outcomes produced by GPT-4. We also adopt a rapid-convergence training strategy to boost search efficiency. Rigorous experimentation corroborates that our algorithm can augment the search efficiency by 2 times under GPT-based scenarios, while also attaining a performance of 2.82 with 0.37 improvement in FID on CIFAR10 relative to the benchmark IDDPM algorithm.

It has been recognized that the data generated by the denoising diffusion probabilistic model (DDPM) improves adversarial training. After two years of rapid development in diffusion models, a question naturally arises: can better diffusion models further improve adversarial training? This paper gives an affirmative answer by employing the most recent diffusion model which has higher efficiency (sim 20 sampling steps) and image quality (lower FID score) compared with DDPM. Our adversarially trained models achieve state-of-the-art performance on RobustBench using only generated data (no external datasets). Under the ell_infty-norm threat model with epsilon=8/255, our models achieve 70.69% and 42.67% robust accuracy on CIFAR-10 and CIFAR-100, respectively, i.e. improving upon previous state-of-the-art models by +4.58% and +8.03%. Under the ell_2-norm threat model with epsilon=128/255, our models achieve 84.86% on CIFAR-10 (+4.44%). These results also beat previous works that use external data. Our code is available at https://github.com/wzekai99/DM-Improves-AT.

Data Augmentation (DA), \ie, synthesizing faithful and diverse samples to expand the original training set, is a prevalent and effective strategy to improve various visual recognition tasks. With the powerful image generation ability, diffusion-based DA has shown strong performance gains on different benchmarks. In this paper, we analyze today's diffusion-based DA methods, and argue that they cannot take account of both faithfulness and diversity, which are two critical keys for generating high-quality samples and boosting final classification performance. To this end, we propose a novel Diffusion-based Inversion Interpolation DA method: Diff-II. Specifically, Diff-II consists of three main steps: 1) Category concepts learning: Learning concept embeddings for each category. 2) Inversion interpolation: Calculating the inversion for each image, and conducting spherical interpolation for two randomly sampled inversions from the same category. 3) Two-stage denoising: Using different prompts to generate synthesized images in a coarse-to-fine manner. Extensive experiments on multiple image classification tasks (\eg, few-shot, long-tailed, and out-of-distribution classification) have demonstrated its effectiveness over state-of-the-art diffusion-based DA methods.

Classifier guidance -- using the gradients of an image classifier to steer the generations of a diffusion model -- has the potential to dramatically expand the creative control over image generation and editing. However, currently classifier guidance requires either training new noise-aware models to obtain accurate gradients or using a one-step denoising approximation of the final generation, which leads to misaligned gradients and sub-optimal control. We highlight this approximation's shortcomings and propose a novel guidance method: Direct Optimization of Diffusion Latents (DOODL), which enables plug-and-play guidance by optimizing diffusion latents w.r.t. the gradients of a pre-trained classifier on the true generated pixels, using an invertible diffusion process to achieve memory-efficient backpropagation. Showcasing the potential of more precise guidance, DOODL outperforms one-step classifier guidance on computational and human evaluation metrics across different forms of guidance: using CLIP guidance to improve generations of complex prompts from DrawBench, using fine-grained visual classifiers to expand the vocabulary of Stable Diffusion, enabling image-conditioned generation with a CLIP visual encoder, and improving image aesthetics using an aesthetic scoring network. Code at https://github.com/salesforce/DOODL.

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs), which enables deterministic inference and exact likelihood evaluation. However, the likelihood estimation results by diffusion ODEs are still far from those of the state-of-the-art likelihood-based generative models. In this work, we propose several improved techniques for maximum likelihood estimation for diffusion ODEs, including both training and evaluation perspectives. For training, we propose velocity parameterization and explore variance reduction techniques for faster convergence. We also derive an error-bounded high-order flow matching objective for finetuning, which improves the ODE likelihood and smooths its trajectory. For evaluation, we propose a novel training-free truncated-normal dequantization to fill the training-evaluation gap commonly existing in diffusion ODEs. Building upon these techniques, we achieve state-of-the-art likelihood estimation results on image datasets (2.56 on CIFAR-10, 3.43/3.69 on ImageNet-32) without variational dequantization or data augmentation.

Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.

Diffusion models are a class of flexible generative models trained with an approximation to the log-likelihood objective. However, most use cases of diffusion models are not concerned with likelihoods, but instead with downstream objectives such as human-perceived image quality or drug effectiveness. In this paper, we investigate reinforcement learning methods for directly optimizing diffusion models for such objectives. We describe how posing denoising as a multi-step decision-making problem enables a class of policy gradient algorithms, which we refer to as denoising diffusion policy optimization (DDPO), that are more effective than alternative reward-weighted likelihood approaches. Empirically, DDPO is able to adapt text-to-image diffusion models to objectives that are difficult to express via prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Finally, we show that DDPO can improve prompt-image alignment using feedback from a vision-language model without the need for additional data collection or human annotation.

Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs require a computationally intensive sampling process that involves the simulation of a (stochastic) differential equation through hundreds of network evaluations. In this work, we take the first step in fast sampling of DDBMs without extra training, motivated by the well-established recipes in diffusion models. We generalize DDBMs via a class of non-Markovian diffusion bridges defined on the discretized timesteps concerning sampling, which share the same marginal distributions and training objectives, give rise to generative processes ranging from stochastic to deterministic, and result in diffusion bridge implicit models (DBIMs). DBIMs are not only up to 25times faster than the vanilla sampler of DDBMs but also induce a novel, simple, and insightful form of ordinary differential equation (ODE) which inspires high-order numerical solvers. Moreover, DBIMs maintain the generation diversity in a distinguished way, by using a booting noise in the initial sampling step, which enables faithful encoding, reconstruction, and semantic interpolation in image translation tasks. Code is available at https://github.com/thu-ml/DiffusionBridge.

This report presents the comprehensive implementation, evaluation, and optimization of Denoising Diffusion Probabilistic Models (DDPMs) and Denoising Diffusion Implicit Models (DDIMs), which are state-of-the-art generative models. During inference, these models take random noise as input and iteratively generate high-quality images as output. The study focuses on enhancing their generative capabilities by incorporating advanced techniques such as Classifier-Free Guidance (CFG), Latent Diffusion Models with Variational Autoencoders (VAE), and alternative noise scheduling strategies. The motivation behind this work is the growing demand for efficient and scalable generative AI models that can produce realistic images across diverse datasets, addressing challenges in applications such as art creation, image synthesis, and data augmentation. Evaluations were conducted on datasets including CIFAR-10 and ImageNet-100, with a focus on improving inference speed, computational efficiency, and image quality metrics like Frechet Inception Distance (FID). Results demonstrate that DDIM + CFG achieves faster inference and superior image quality. Challenges with VAE and noise scheduling are also highlighted, suggesting opportunities for future optimization. This work lays the groundwork for developing scalable, efficient, and high-quality generative AI systems to benefit industries ranging from entertainment to robotics.

We introduce a Cascaded Diffusion Model (Cas-DM) that improves a Denoising Diffusion Probabilistic Model (DDPM) by effectively incorporating additional metric functions in training. Metric functions such as the LPIPS loss have been proven highly effective in consistency models derived from the score matching. However, for the diffusion counterparts, the methodology and efficacy of adding extra metric functions remain unclear. One major challenge is the mismatch between the noise predicted by a DDPM at each step and the desired clean image that the metric function works well on. To address this problem, we propose Cas-DM, a network architecture that cascades two network modules to effectively apply metric functions to the diffusion model training. The first module, similar to a standard DDPM, learns to predict the added noise and is unaffected by the metric function. The second cascaded module learns to predict the clean image, thereby facilitating the metric function computation. Experiment results show that the proposed diffusion model backbone enables the effective use of the LPIPS loss, leading to state-of-the-art image quality (FID, sFID, IS) on various established benchmarks.

Imitation learning aims to learn a policy from observing expert demonstrations without access to reward signals from environments. Generative adversarial imitation learning (GAIL) formulates imitation learning as adversarial learning, employing a generator policy learning to imitate expert behaviors and discriminator learning to distinguish the expert demonstrations from agent trajectories. Despite its encouraging results, GAIL training is often brittle and unstable. Inspired by the recent dominance of diffusion models in generative modeling, this work proposes Diffusion-Reward Adversarial Imitation Learning (DRAIL), which integrates a diffusion model into GAIL, aiming to yield more precise and smoother rewards for policy learning. Specifically, we propose a diffusion discriminative classifier to construct an enhanced discriminator; then, we design diffusion rewards based on the classifier's output for policy learning. We conduct extensive experiments in navigation, manipulation, and locomotion, verifying DRAIL's effectiveness compared to prior imitation learning methods. Moreover, additional experimental results demonstrate the generalizability and data efficiency of DRAIL. Visualized learned reward functions of GAIL and DRAIL suggest that DRAIL can produce more precise and smoother rewards.

This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We provide a detailed basic mathematical framework for DDPMs and explain the main ideas behind training and generation procedures. In this overview article we also review selected extensions and improvements of the basic framework from the literature such as improved DDPMs, denoising diffusion implicit models, classifier-free diffusion guidance models, and latent diffusion models.

Diffusion models have achieved great success in a range of tasks, such as image synthesis and molecule design. As such successes hinge on large-scale training data collected from diverse sources, the trustworthiness of these collected data is hard to control or audit. In this work, we aim to explore the vulnerabilities of diffusion models under potential training data manipulations and try to answer: How hard is it to perform Trojan attacks on well-trained diffusion models? What are the adversarial targets that such Trojan attacks can achieve? To answer these questions, we propose an effective Trojan attack against diffusion models, TrojDiff, which optimizes the Trojan diffusion and generative processes during training. In particular, we design novel transitions during the Trojan diffusion process to diffuse adversarial targets into a biased Gaussian distribution and propose a new parameterization of the Trojan generative process that leads to an effective training objective for the attack. In addition, we consider three types of adversarial targets: the Trojaned diffusion models will always output instances belonging to a certain class from the in-domain distribution (In-D2D attack), out-of-domain distribution (Out-D2D-attack), and one specific instance (D2I attack). We evaluate TrojDiff on CIFAR-10 and CelebA datasets against both DDPM and DDIM diffusion models. We show that TrojDiff always achieves high attack performance under different adversarial targets using different types of triggers, while the performance in benign environments is preserved. The code is available at https://github.com/chenweixin107/TrojDiff.

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to reinterpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection-error of the denoiser. Finally, we propose a new sampler based on two simple modifications to DDIM using insights from our theoretical results. In as few as 5-10 function evaluations, our sampler achieves state-of-the-art FID scores on pretrained CIFAR-10 and CelebA models and can generate high quality samples on latent diffusion models.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is generated, it cannot be updated again, even when it introduces an error. Here, we address this limitation by introducing the remasking diffusion model (ReMDM) sampler, a method that can be applied to pretrained masked diffusion models in a principled way and that is derived from a discrete diffusion model with a custom remasking backward process. Most interestingly, ReMDM endows discrete diffusion with a form of inference-time compute scaling. By increasing the number of sampling steps, ReMDM generates natural language outputs that approach the quality of autoregressive models, whereas when the computation budget is limited, ReMDM better maintains quality. ReMDM also improves sample quality of masked diffusion models for discretized images, and in scientific domains such as molecule design, ReMDM facilitates diffusion guidance and pushes the Pareto frontier of controllability relative to classical masking and uniform noise diffusion. We provide the code along with a blog post on the project page: https://remdm.github.io.

The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving either the probability flow ODE or diffusion SDE wherein a neural network approximates the score function allowing a numerical ODE/SDE solver to be used. However, naive backpropagation techniques are memory intensive, requiring the storage of all intermediate states, and face additional complexity in handling the injected noise from the diffusion term of the diffusion SDE. We propose a novel family of bespoke ODE solvers to the continuous adjoint equations for diffusion models, which we call AdjointDEIS. We exploit the unique construction of diffusion SDEs to further simplify the formulation of the continuous adjoint equations using exponential integrators. Moreover, we provide convergence order guarantees for our bespoke solvers. Significantly, we show that continuous adjoint equations for diffusion SDEs actually simplify to a simple ODE. Lastly, we demonstrate the effectiveness of AdjointDEIS for guided generation with an adversarial attack in the form of the face morphing problem. Our code will be released on our project page https://zblasingame.github.io/AdjointDEIS/

The gradual nature of a diffusion process that synthesizes samples in small increments constitutes a key ingredient of Denoising Diffusion Probabilistic Models (DDPM), which have presented unprecedented quality in image synthesis and been recently explored in the motion domain. In this work, we propose to adapt the gradual diffusion concept (operating along a diffusion time-axis) into the temporal-axis of the motion sequence. Our key idea is to extend the DDPM framework to support temporally varying denoising, thereby entangling the two axes. Using our special formulation, we iteratively denoise a motion buffer that contains a set of increasingly-noised poses, which auto-regressively produces an arbitrarily long stream of frames. With a stationary diffusion time-axis, in each diffusion step we increment only the temporal-axis of the motion such that the framework produces a new, clean frame which is removed from the beginning of the buffer, followed by a newly drawn noise vector that is appended to it. This new mechanism paves the way towards a new framework for long-term motion synthesis with applications to character animation and other domains.

Denoising diffusion probabilistic models have transformed image generation with their impressive fidelity and diversity. We show that they also excel in estimating optical flow and monocular depth, surprisingly, without task-specific architectures and loss functions that are predominant for these tasks. Compared to the point estimates of conventional regression-based methods, diffusion models also enable Monte Carlo inference, e.g., capturing uncertainty and ambiguity in flow and depth. With self-supervised pre-training, the combined use of synthetic and real data for supervised training, and technical innovations (infilling and step-unrolled denoising diffusion training) to handle noisy-incomplete training data, and a simple form of coarse-to-fine refinement, one can train state-of-the-art diffusion models for depth and optical flow estimation. Extensive experiments focus on quantitative performance against benchmarks, ablations, and the model's ability to capture uncertainty and multimodality, and impute missing values. Our model, DDVM (Denoising Diffusion Vision Model), obtains a state-of-the-art relative depth error of 0.074 on the indoor NYU benchmark and an Fl-all outlier rate of 3.26\% on the KITTI optical flow benchmark, about 25\% better than the best published method. For an overview see https://diffusion-vision.github.io.

Discrete diffusion models have achieved success in tasks like image generation and masked language modeling but face limitations in controlled content editing. We introduce DICE (Discrete Inversion for Controllable Editing), the first approach to enable precise inversion for discrete diffusion models, including multinomial diffusion and masked generative models. By recording noise sequences and masking patterns during the reverse diffusion process, DICE enables accurate reconstruction and flexible editing of discrete data without the need for predefined masks or attention manipulation. We demonstrate the effectiveness of DICE across both image and text domains, evaluating it on models such as VQ-Diffusion, Paella, and RoBERTa. Our results show that DICE preserves high data fidelity while enhancing editing capabilities, offering new opportunities for fine-grained content manipulation in discrete spaces. For project webpage, see https://hexiaoxiao-cs.github.io/DICE/.

We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Common image-to-image translation methods rely on joint training over data from both source and target domains. The training process requires concurrent access to both datasets, which hinders data separation and privacy protection; and existing models cannot be easily adapted for translation of new domain pairs. We present Dual Diffusion Implicit Bridges (DDIBs), an image translation method based on diffusion models, that circumvents training on domain pairs. Image translation with DDIBs relies on two diffusion models trained independently on each domain, and is a two-step process: DDIBs first obtain latent encodings for source images with the source diffusion model, and then decode such encodings using the target model to construct target images. Both steps are defined via ordinary differential equations (ODEs), thus the process is cycle consistent only up to discretization errors of the ODE solvers. Theoretically, we interpret DDIBs as concatenation of source to latent, and latent to target Schrodinger Bridges, a form of entropy-regularized optimal transport, to explain the efficacy of the method. Experimentally, we apply DDIBs on synthetic and high-resolution image datasets, to demonstrate their utility in a wide variety of translation tasks and their inherent optimal transport properties.

Despite recent advances in inversion-based editing, text-guided image manipulation remains challenging for diffusion models. The primary bottlenecks include 1) the time-consuming nature of the inversion process; 2) the struggle to balance consistency with accuracy; 3) the lack of compatibility with efficient consistency sampling methods used in consistency models. To address the above issues, we start by asking ourselves if the inversion process can be eliminated for editing. We show that when the initial sample is known, a special variance schedule reduces the denoising step to the same form as the multi-step consistency sampling. We name this Denoising Diffusion Consistent Model (DDCM), and note that it implies a virtual inversion strategy without explicit inversion in sampling. We further unify the attention control mechanisms in a tuning-free framework for text-guided editing. Combining them, we present inversion-free editing (InfEdit), which allows for consistent and faithful editing for both rigid and non-rigid semantic changes, catering to intricate modifications without compromising on the image's integrity and explicit inversion. Through extensive experiments, InfEdit shows strong performance in various editing tasks and also maintains a seamless workflow (less than 3 seconds on one single A40), demonstrating the potential for real-time applications. Project Page: https://sled-group.github.io/InfEdit/

In medical imaging, the diffusion models have shown great potential in synthetic image generation tasks. However, these models often struggle with the interpretable connections between the generated and existing images and could create illusions. To address these challenges, our research proposes a novel diffusion-based generative model based on deformation diffusion and recovery. This model, named Deformation-Recovery Diffusion Model (DRDM), diverges from traditional score/intensity and latent feature-based approaches, emphasizing morphological changes through deformation fields rather than direct image synthesis. This is achieved by introducing a topological-preserving deformation field generation method, which randomly samples and integrates a set of multi-scale Deformation Vector Fields (DVF). DRDM is trained to learn to recover unreasonable deformation components, thereby restoring each randomly deformed image to a realistic distribution. These innovations facilitate the generation of diverse and anatomically plausible deformations, enhancing data augmentation and synthesis for further analysis in downstream tasks, such as few-shot learning and image registration. Experimental results in cardiac MRI and pulmonary CT show DRDM is capable of creating diverse, large (over 10\% image size deformation scale), and high-quality (negative rate of the Jacobian matrix's determinant is lower than 1\%) deformation fields. The further experimental results in downstream tasks, 2D image segmentation and 3D image registration, indicate significant improvements resulting from DRDM, showcasing the potential of our model to advance image manipulation and synthesis in medical imaging and beyond. Project page: https://jianqingzheng.github.io/def_diff_rec/

Low-quality or scarce data has posed significant challenges for training deep neural networks in practice. While classical data augmentation cannot contribute very different new data, diffusion models opens up a new door to build self-evolving AI by generating high-quality and diverse synthetic data through text-guided prompts. However, text-only guidance cannot control synthetic images' proximity to the original images, resulting in out-of-distribution data detrimental to the model performance. To overcome the limitation, we study image guidance to achieve a spectrum of interpolations between synthetic and real images. With stronger image guidance, the generated images are similar to the training data but hard to learn. While with weaker image guidance, the synthetic images will be easier for model but contribute to a larger distribution gap with the original data. The generated full spectrum of data enables us to build a novel "Diffusion Curriculum (DisCL)". DisCL adjusts the image guidance level of image synthesis for each training stage: It identifies and focuses on hard samples for the model and assesses the most effective guidance level of synthetic images to improve hard data learning. We apply DisCL to two challenging tasks: long-tail (LT) classification and learning from low-quality data. It focuses on lower-guidance images of high-quality to learn prototypical features as a warm-up of learning higher-guidance images that might be weak on diversity or quality. Extensive experiments showcase a gain of 2.7% and 2.1% in OOD and ID macro-accuracy when applying DisCL to iWildCam dataset. On ImageNet-LT, DisCL improves the base model's tail-class accuracy from 4.4% to 23.64% and leads to a 4.02% improvement in all-class accuracy.

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on diffusion bridges, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.

Computed tomography (CT) serves as an effective tool for lung cancer screening, diagnosis, treatment, and prognosis, providing a rich source of features to quantify temporal and spatial tumor changes. Nonetheless, the diversity of CT scanners and customized acquisition protocols can introduce significant inconsistencies in texture features, even when assessing the same patient. This variability poses a fundamental challenge for subsequent research that relies on consistent image features. Existing CT image standardization models predominantly utilize GAN-based supervised or semi-supervised learning, but their performance remains limited. We present DiffusionCT, an innovative score-based DDPM model that operates in the latent space to transform disparate non-standard distributions into a standardized form. The architecture comprises a U-Net-based encoder-decoder, augmented by a DDPM model integrated at the bottleneck position. First, the encoder-decoder is trained independently, without embedding DDPM, to capture the latent representation of the input data. Second, the latent DDPM model is trained while keeping the encoder-decoder parameters fixed. Finally, the decoder uses the transformed latent representation to generate a standardized CT image, providing a more consistent basis for downstream analysis. Empirical tests on patient CT images indicate notable improvements in image standardization using DiffusionCT. Additionally, the model significantly reduces image noise in SPAD images, further validating the effectiveness of DiffusionCT for advanced imaging tasks.

Plug-and-play Image Restoration (IR) has been widely recognized as a flexible and interpretable method for solving various inverse problems by utilizing any off-the-shelf denoiser as the implicit image prior. However, most existing methods focus on discriminative Gaussian denoisers. Although diffusion models have shown impressive performance for high-quality image synthesis, their potential to serve as a generative denoiser prior to the plug-and-play IR methods remains to be further explored. While several other attempts have been made to adopt diffusion models for image restoration, they either fail to achieve satisfactory results or typically require an unacceptable number of Neural Function Evaluations (NFEs) during inference. This paper proposes DiffPIR, which integrates the traditional plug-and-play method into the diffusion sampling framework. Compared to plug-and-play IR methods that rely on discriminative Gaussian denoisers, DiffPIR is expected to inherit the generative ability of diffusion models. Experimental results on three representative IR tasks, including super-resolution, image deblurring, and inpainting, demonstrate that DiffPIR achieves state-of-the-art performance on both the FFHQ and ImageNet datasets in terms of reconstruction faithfulness and perceptual quality with no more than 100 NFEs. The source code is available at {https://github.com/yuanzhi-zhu/DiffPIR}

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based scheme to make the time schedule in sampling better fit the underlying trajectory structure. This simple strategy requires minimal modification to any given ODE-based numerical solvers and incurs negligible computational cost, while delivering superior performance in image generation, especially in 5sim 10 function evaluations.

In this paper, we point out suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscible phenomenon in physics, we propose Immiscible Diffusion, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of the molecular sources is distinguishable. Inspired by this, we propose an assignment-then-diffusion training strategy. Specifically, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to separate the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. This ensures that each image is projected only to nearby noise. To address the high complexity of the assignment algorithm, we employ a quantized-assignment method to reduce the computational overhead to a negligible level. Experiments demonstrate that our method achieve up to 3x faster training for consistency models and DDIM on the CIFAR dataset, and up to 1.3x faster on CelebA datasets for consistency models. Besides, we conduct thorough analysis about the Immiscible Diffusion, which sheds lights on how it improves diffusion training speed while improving the fidelity.

Guidance in conditional diffusion generation is of great importance for sample quality and controllability. However, existing guidance schemes are to be desired. On one hand, mainstream methods such as classifier guidance and classifier-free guidance both require extra training with labeled data, which is time-consuming and unable to adapt to new conditions. On the other hand, training-free methods such as universal guidance, though more flexible, have yet to demonstrate comparable performance. In this work, through a comprehensive investigation into the design space, we show that it is possible to achieve significant performance improvements over existing guidance schemes by leveraging off-the-shelf classifiers in a training-free fashion, enjoying the best of both worlds. Employing calibration as a general guideline, we propose several pre-conditioning techniques to better exploit pretrained off-the-shelf classifiers for guiding diffusion generation. Extensive experiments on ImageNet validate our proposed method, showing that state-of-the-art diffusion models (DDPM, EDM, DiT) can be further improved (up to 20%) using off-the-shelf classifiers with barely any extra computational cost. With the proliferation of publicly available pretrained classifiers, our proposed approach has great potential and can be readily scaled up to text-to-image generation tasks. The code is available at https://github.com/AlexMaOLS/EluCD/tree/main.

Text-guided diffusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. We address these challenges by investigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as a key issue. To resolve this, we introduce the Logistic Schedule, a novel noise schedule designed to eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity compared to traditional noise schedules, highlighting its adaptability and effectiveness.

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the system state will evolve over time, and the design challenge is to optimize the initial conditions that lead to a target outcome. Recent developments in learned simulation have shown that graph neural networks (GNNs) can be used for accurate, efficient, differentiable estimation of simulator dynamics, and support high-quality design optimization with gradient- or sampling-based optimization procedures. However, optimizing designs from scratch requires many expensive model queries, and these procedures exhibit basic failures on either non-convex or high-dimensional problems.In this work, we show how denoising diffusion models (DDMs) can be used to solve inverse design problems efficiently and propose a particle sampling algorithm for further improving their efficiency. We perform experiments on a number of fluid dynamics design challenges, and find that our approach substantially reduces the number of calls to the simulator compared to standard techniques.

The development of video diffusion models unveils a significant challenge: the substantial computational demands. To mitigate this challenge, we note that the reverse process of diffusion exhibits an inherent entropy-reducing nature. Given the inter-frame redundancy in video modality, maintaining full frame rates in high-entropy stages is unnecessary. Based on this insight, we propose TPDiff, a unified framework to enhance training and inference efficiency. By dividing diffusion into several stages, our framework progressively increases frame rate along the diffusion process with only the last stage operating on full frame rate, thereby optimizing computational efficiency. To train the multi-stage diffusion model, we introduce a dedicated training framework: stage-wise diffusion. By solving the partitioned probability flow ordinary differential equations (ODE) of diffusion under aligned data and noise, our training strategy is applicable to various diffusion forms and further enhances training efficiency. Comprehensive experimental evaluations validate the generality of our method, demonstrating 50% reduction in training cost and 1.5x improvement in inference efficiency.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

Despite the ever-increasing interest in applying deep learning (DL) models to medical imaging, the typical scarcity and imbalance of medical datasets can severely impact the performance of DL models. The generation of synthetic data that might be freely shared without compromising patient privacy is a well-known technique for addressing these difficulties. Inpainting algorithms are a subset of DL generative models that can alter one or more regions of an input image while matching its surrounding context and, in certain cases, non-imaging input conditions. Although the majority of inpainting techniques for medical imaging data use generative adversarial networks (GANs), the performance of these algorithms is frequently suboptimal due to their limited output variety, a problem that is already well-known for GANs. Denoising diffusion probabilistic models (DDPMs) are a recently introduced family of generative networks that can generate results of comparable quality to GANs, but with diverse outputs. In this paper, we describe a DDPM to execute multiple inpainting tasks on 2D axial slices of brain MRI with various sequences, and present proof-of-concept examples of its performance in a variety of evaluation scenarios. Our model and a public online interface to try our tool are available at: https://github.com/Mayo-Radiology-Informatics-Lab/MBTI

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding techniques for boundary enforcement. Reflected diffusion models (Lou23) aim to enhance generalizability by generating the data distribution through a backward process governed by reflected Brownian motion. However, reflected diffusion models may not easily adapt to diverse domains without the derivation of proper diffeomorphic mappings and do not guarantee optimal transport properties. To overcome these limitations, we introduce the Reflected Schrodinger Bridge algorithm: an entropy-regularized optimal transport approach tailored for generating data within diverse bounded domains. We derive elegant reflected forward-backward stochastic differential equations with Neumann and Robin boundary conditions, extend divergence-based likelihood training to bounded domains, and explore natural connections to entropic optimal transport for the study of approximate linear convergence - a valuable insight for practical training. Our algorithm yields robust generative modeling in diverse domains, and its scalability is demonstrated in real-world constrained generative modeling through standard image benchmarks.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

This paper describes an efficient algorithm for solving noisy linear inverse problems using pretrained diffusion models. Extending the paradigm of denoising diffusion implicit models (DDIM), we propose constrained diffusion implicit models (CDIM) that modify the diffusion updates to enforce a constraint upon the final output. For noiseless inverse problems, CDIM exactly satisfies the constraints; in the noisy case, we generalize CDIM to satisfy an exact constraint on the residual distribution of the noise. Experiments across a variety of tasks and metrics show strong performance of CDIM, with analogous inference acceleration to unconstrained DDIM: 10 to 50 times faster than previous conditional diffusion methods. We demonstrate the versatility of our approach on many problems including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reconstruction.

Recent developments in offline reinforcement learning have uncovered the immense potential of diffusion modeling, which excels at representing heterogeneous behavior policies. However, sampling from diffusion policies is considerably slow because it necessitates tens to hundreds of iterative inference steps for one action. To address this issue, we propose to extract an efficient deterministic inference policy from critic models and pretrained diffusion behavior models, leveraging the latter to directly regularize the policy gradient with the behavior distribution's score function during optimization. Our method enjoys powerful generative capabilities of diffusion modeling while completely circumventing the computationally intensive and time-consuming diffusion sampling scheme, both during training and evaluation. Extensive results on D4RL tasks show that our method boosts action sampling speed by more than 25 times compared with various leading diffusion-based methods in locomotion tasks, while still maintaining state-of-the-art performance.

Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs and GANs cover the target distribution. Finally, we show that the sample quality and likelihood of these models scale smoothly with model capacity and training compute, making them easily scalable. We release our code at https://github.com/openai/improved-diffusion

Large-scale Text-to-Image (T2I) diffusion models have revolutionized image generation over the last few years. Although owning diverse and high-quality generation capabilities, translating these abilities to fine-grained image editing remains challenging. In this paper, we propose DiffEditor to rectify two weaknesses in existing diffusion-based image editing: (1) in complex scenarios, editing results often lack editing accuracy and exhibit unexpected artifacts; (2) lack of flexibility to harmonize editing operations, e.g., imagine new content. In our solution, we introduce image prompts in fine-grained image editing, cooperating with the text prompt to better describe the editing content. To increase the flexibility while maintaining content consistency, we locally combine stochastic differential equation (SDE) into the ordinary differential equation (ODE) sampling. In addition, we incorporate regional score-based gradient guidance and a time travel strategy into the diffusion sampling, further improving the editing quality. Extensive experiments demonstrate that our method can efficiently achieve state-of-the-art performance on various fine-grained image editing tasks, including editing within a single image (e.g., object moving, resizing, and content dragging) and across images (e.g., appearance replacing and object pasting). Our source code is released at https://github.com/MC-E/DragonDiffusion.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

Sketch-based terrain generation seeks to create realistic landscapes for virtual environments in various applications such as computer games, animation and virtual reality. Recently, deep learning based terrain generation has emerged, notably the ones based on generative adversarial networks (GAN). However, these methods often struggle to fulfill the requirements of flexible user control and maintain generative diversity for realistic terrain. Therefore, we propose a novel diffusion-based method, namely terrain diffusion network (TDN), which actively incorporates user guidance for enhanced controllability, taking into account terrain features like rivers, ridges, basins, and peaks. Instead of adhering to a conventional monolithic denoising process, which often compromises the fidelity of terrain details or the alignment with user control, a multi-level denoising scheme is proposed to generate more realistic terrains by taking into account fine-grained details, particularly those related to climatic patterns influenced by erosion and tectonic activities. Specifically, three terrain synthesisers are designed for structural, intermediate, and fine-grained level denoising purposes, which allow each synthesiser concentrate on a distinct terrain aspect. Moreover, to maximise the efficiency of our TDN, we further introduce terrain and sketch latent spaces for the synthesizers with pre-trained terrain autoencoders. Comprehensive experiments on a new dataset constructed from NASA Topology Images clearly demonstrate the effectiveness of our proposed method, achieving the state-of-the-art performance. Our code and dataset will be publicly available.

Magnetic resonance imaging (MRI) is a common and life-saving medical imaging technique. However, acquiring high signal-to-noise ratio MRI scans requires long scan times, resulting in increased costs and patient discomfort, and decreased throughput. Thus, there is great interest in denoising MRI scans, especially for the subtype of diffusion MRI scans that are severely SNR-limited. While most prior MRI denoising methods are supervised in nature, acquiring supervised training datasets for the multitude of anatomies, MRI scanners, and scan parameters proves impractical. Here, we propose Denoising Diffusion Models for Denoising Diffusion MRI (DDM^2), a self-supervised denoising method for MRI denoising using diffusion denoising generative models. Our three-stage framework integrates statistic-based denoising theory into diffusion models and performs denoising through conditional generation. During inference, we represent input noisy measurements as a sample from an intermediate posterior distribution within the diffusion Markov chain. We conduct experiments on 4 real-world in-vivo diffusion MRI datasets and show that our DDM^2 demonstrates superior denoising performances ascertained with clinically-relevant visual qualitative and quantitative metrics.

Diffusion models have been used extensively for high quality image and video generation tasks. In this paper, we propose a novel conditional diffusion model with spatial attention and latent embedding (cDAL) for medical image segmentation. In cDAL, a convolutional neural network (CNN) based discriminator is used at every time-step of the diffusion process to distinguish between the generated labels and the real ones. A spatial attention map is computed based on the features learned by the discriminator to help cDAL generate more accurate segmentation of discriminative regions in an input image. Additionally, we incorporated a random latent embedding into each layer of our model to significantly reduce the number of training and sampling time-steps, thereby making it much faster than other diffusion models for image segmentation. We applied cDAL on 3 publicly available medical image segmentation datasets (MoNuSeg, Chest X-ray and Hippocampus) and observed significant qualitative and quantitative improvements with higher Dice scores and mIoU over the state-of-the-art algorithms. The source code is publicly available at https://github.com/Hejrati/cDAL/.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

We introduce Interleaved Gibbs Diffusion (IGD), a novel generative modeling framework for mixed continuous-discrete data, focusing on constrained generation problems. Prior works on discrete and continuous-discrete diffusion models assume factorized denoising distribution for fast generation, which can hinder the modeling of strong dependencies between random variables encountered in constrained generation. IGD moves beyond this by interleaving continuous and discrete denoising algorithms via a discrete time Gibbs sampling type Markov chain. IGD provides flexibility in the choice of denoisers, allows conditional generation via state-space doubling and inference time scaling via the ReDeNoise method. Empirical evaluations on three challenging tasks-solving 3-SAT, generating molecule structures, and generating layouts-demonstrate state-of-the-art performance. Notably, IGD achieves a 7% improvement on 3-SAT out of the box and achieves state-of-the-art results in molecule generation without relying on equivariant diffusion or domain-specific architectures. We explore a wide range of modeling, and interleaving strategies along with hyperparameters in each of these problems.

Satellite remote sensing missions have gained popularity over the past fifteen years due to their ability to cover large swaths of land at regular intervals, making them ideal for monitoring environmental trends. The FINCH mission, a 3U+ CubeSat equipped with a hyperspectral camera, aims to monitor crop residue cover in agricultural fields. Although hyperspectral imaging captures both spectral and spatial information, it is prone to various types of noise, including random noise, stripe noise, and dead pixels. Effective denoising of these images is crucial for downstream scientific tasks. Traditional methods, including hand-crafted techniques encoding strong priors, learned 2D image denoising methods applied across different hyperspectral bands, or diffusion generative models applied independently on bands, often struggle with varying noise strengths across spectral bands, leading to significant spectral distortion. This paper presents a novel approach to hyperspectral image denoising using latent diffusion models that integrate spatial and spectral information. We particularly do so by building a 3D diffusion model and presenting a 3-stage training approach on real and synthetically crafted datasets. The proposed method preserves image structure while reducing noise. Evaluations on both popular hyperspectral denoising datasets and synthetically crafted datasets for the FINCH mission demonstrate the effectiveness of this approach.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset, and a 4sim 16times speedup compared with previous state-of-the-art training-free samplers on various datasets.

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

Material reconstruction from a photograph is a key component of 3D content creation democratization. We propose to formulate this ill-posed problem as a controlled synthesis one, leveraging the recent progress in generative deep networks. We present ControlMat, a method which, given a single photograph with uncontrolled illumination as input, conditions a diffusion model to generate plausible, tileable, high-resolution physically-based digital materials. We carefully analyze the behavior of diffusion models for multi-channel outputs, adapt the sampling process to fuse multi-scale information and introduce rolled diffusion to enable both tileability and patched diffusion for high-resolution outputs. Our generative approach further permits exploration of a variety of materials which could correspond to the input image, mitigating the unknown lighting conditions. We show that our approach outperforms recent inference and latent-space-optimization methods, and carefully validate our diffusion process design choices. Supplemental materials and additional details are available at: https://gvecchio.com/controlmat/.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

Conditional diffusion models have demonstrated impressive performance in image manipulation tasks. The general pipeline involves adding noise to the image and then denoising it. However, this method faces a trade-off problem: adding too much noise affects the fidelity of the image while adding too little affects its editability. This largely limits their practical applicability. In this paper, we propose a novel framework, Selective Diffusion Distillation (SDD), that ensures both the fidelity and editability of images. Instead of directly editing images with a diffusion model, we train a feedforward image manipulation network under the guidance of the diffusion model. Besides, we propose an effective indicator to select the semantic-related timestep to obtain the correct semantic guidance from the diffusion model. This approach successfully avoids the dilemma caused by the diffusion process. Our extensive experiments demonstrate the advantages of our framework. Code is released at https://github.com/AndysonYs/Selective-Diffusion-Distillation.

The rapid advancement of Artificial Intelligence (AI) in biomedical imaging and radiotherapy is hindered by the limited availability of large imaging data repositories. With recent research and improvements in denoising diffusion probabilistic models (DDPM), high quality synthetic medical scans are now possible. Despite this, there is currently no way of generating multiple related images, such as a corresponding ground truth which can be used to train models, so synthetic scans are often manually annotated before use. This research introduces a novel architecture that is able to generate multiple, related PET-CT-tumour mask pairs using paired networks and conditional encoders. Our approach includes innovative, time step-controlled mechanisms and a `noise-seeding' strategy to improve DDPM sampling consistency. While our model requires a modified perceptual loss function to ensure accurate feature alignment we show generation of clearly aligned synthetic images and improvement in segmentation accuracy with generated images.

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT

Denoising Diffusion Probabilistic Models (DDPMs) achieve state-of-the-art performance in synthesizing new images from random noise, but they lack meaningful latent space that encodes data into features. Recent DDPM-based editing techniques try to mitigate this issue by inverting images back to their approximated staring noise. In this work, we study the relation between the initial Gaussian noise, the samples generated from it, and their corresponding latent encodings obtained through the inversion procedure. First, we interpret their spatial distance relations to show the inaccuracy of the DDIM inversion technique by localizing latent representations manifold between the initial noise and generated samples. Then, we demonstrate the peculiar relation between initial Gaussian noise and its corresponding generations during diffusion training, showing that the high-level features of generated images stabilize rapidly, keeping the spatial distance relationship between noises and generations consistent throughout the training.

Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the Controlled Monte Carlo Diffusion sampler (CMCD) for Bayesian computation, a score-based annealing technique that crucially adapts both forward and backward dynamics in a diffusion model. On the way, we clarify the relationship between the EM-algorithm and iterative proportional fitting (IPF) for Schr{\"o}dinger bridges, deriving as well a regularised objective that bypasses the iterative bottleneck of standard IPF-updates. Finally, we show that CMCD has a strong foundation in the Jarzinsky and Crooks identities from statistical physics, and that it convincingly outperforms competing approaches across a wide array of experiments.

Diffusion models are the main driver of progress in image and video synthesis, but suffer from slow inference speed. Distillation methods, like the recently introduced adversarial diffusion distillation (ADD) aim to shift the model from many-shot to single-step inference, albeit at the cost of expensive and difficult optimization due to its reliance on a fixed pretrained DINOv2 discriminator. We introduce Latent Adversarial Diffusion Distillation (LADD), a novel distillation approach overcoming the limitations of ADD. In contrast to pixel-based ADD, LADD utilizes generative features from pretrained latent diffusion models. This approach simplifies training and enhances performance, enabling high-resolution multi-aspect ratio image synthesis. We apply LADD to Stable Diffusion 3 (8B) to obtain SD3-Turbo, a fast model that matches the performance of state-of-the-art text-to-image generators using only four unguided sampling steps. Moreover, we systematically investigate its scaling behavior and demonstrate LADD's effectiveness in various applications such as image editing and inpainting.

When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

We present Diffusion Model Patching (DMP), a simple method to boost the performance of pre-trained diffusion models that have already reached convergence, with a negligible increase in parameters. DMP inserts a small, learnable set of prompts into the model's input space while keeping the original model frozen. The effectiveness of DMP is not merely due to the addition of parameters but stems from its dynamic gating mechanism, which selects and combines a subset of learnable prompts at every step of the generative process (e.g., reverse denoising steps). This strategy, which we term "mixture-of-prompts", enables the model to draw on the distinct expertise of each prompt, essentially "patching" the model's functionality at every step with minimal yet specialized parameters. Uniquely, DMP enhances the model by further training on the same dataset on which it was originally trained, even in a scenario where significant improvements are typically not expected due to model convergence. Experiments show that DMP significantly enhances the converged FID of DiT-L/2 on FFHQ 256x256 by 10.38%, achieved with only a 1.43% parameter increase and 50K additional training iterations.

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.

Diffusion models (DMs) excel in photorealism, image editing, and solving inverse problems, aided by classifier-free guidance and image inversion techniques. However, rectified flow models (RFMs) remain underexplored for these tasks. Existing DM-based methods often require additional training, lack generalization to pretrained latent models, underperform, and demand significant computational resources due to extensive backpropagation through ODE solvers and inversion processes. In this work, we first develop a theoretical and empirical understanding of the vector field dynamics of RFMs in efficiently guiding the denoising trajectory. Our findings reveal that we can navigate the vector field in a deterministic and gradient-free manner. Utilizing this property, we propose FlowChef, which leverages the vector field to steer the denoising trajectory for controlled image generation tasks, facilitated by gradient skipping. FlowChef is a unified framework for controlled image generation that, for the first time, simultaneously addresses classifier guidance, linear inverse problems, and image editing without the need for extra training, inversion, or intensive backpropagation. Finally, we perform extensive evaluations and show that FlowChef significantly outperforms baselines in terms of performance, memory, and time requirements, achieving new state-of-the-art results. Project Page: https://flowchef.github.io.

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the fixed linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories. This exploration underscores NFDM's versatility and its potential for a wide range of applications.

Diffusion Models (DM) have democratized AI image generation through an iterative denoising process. Quantization is a major technique to alleviate the inference cost and reduce the size of DM denoiser networks. However, as denoisers evolve from variants of convolutional U-Nets toward newer Transformer architectures, it is of growing importance to understand the quantization sensitivity of different weight layers, operations and architecture types to performance. In this work, we address this challenge with Qua^2SeDiMo, a mixed-precision Post-Training Quantization framework that generates explainable insights on the cost-effectiveness of various model weight quantization methods for different denoiser operation types and block structures. We leverage these insights to make high-quality mixed-precision quantization decisions for a myriad of diffusion models ranging from foundational U-Nets to state-of-the-art Transformers. As a result, Qua^2SeDiMo can construct 3.4-bit, 3.9-bit, 3.65-bit and 3.7-bit weight quantization on PixArt-{alpha}, PixArt-{Sigma}, Hunyuan-DiT and SDXL, respectively. We further pair our weight-quantization configurations with 6-bit activation quantization and outperform existing approaches in terms of quantitative metrics and generative image quality.

Image-based virtual try-on (VTON), which aims to generate an outfitted image of a target human wearing an in-shop garment, is a challenging image-synthesis task calling for not only high fidelity of the outfitted human but also full preservation of garment details. To tackle this issue, we propose Outfitting over Try-on Diffusion (OOTDiffusion), leveraging the power of pretrained latent diffusion models and designing a novel network architecture for realistic and controllable virtual try-on. Without an explicit warping process, we propose an outfitting UNet to learn the garment detail features, and merge them with the target human body via our proposed outfitting fusion in the denoising process of diffusion models. In order to further enhance the controllability of our outfitting UNet, we introduce outfitting dropout to the training process, which enables us to adjust the strength of garment features through classifier-free guidance. Our comprehensive experiments on the VITON-HD and Dress Code datasets demonstrate that OOTDiffusion efficiently generates high-quality outfitted images for arbitrary human and garment images, which outperforms other VTON methods in both fidelity and controllability, indicating an impressive breakthrough in virtual try-on. Our source code is available at https://github.com/levihsu/OOTDiffusion.

Denoising diffusion probabilistic models (DDPMs) have achieved high quality image generation without adversarial training, yet they require simulating a Markov chain for many steps to produce a sample. To accelerate sampling, we present denoising diffusion implicit models (DDIMs), a more efficient class of iterative implicit probabilistic models with the same training procedure as DDPMs. In DDPMs, the generative process is defined as the reverse of a Markovian diffusion process. We construct a class of non-Markovian diffusion processes that lead to the same training objective, but whose reverse process can be much faster to sample from. We empirically demonstrate that DDIMs can produce high quality samples 10 times to 50 times faster in terms of wall-clock time compared to DDPMs, allow us to trade off computation for sample quality, and can perform semantically meaningful image interpolation directly in the latent space.

Diffusion models have recently received a surge of interest due to their impressive performance for image restoration, especially in terms of noise robustness. However, existing diffusion-based methods are trained on a large amount of training data and perform very well in-distribution, but can be quite susceptible to distribution shift. This is especially inappropriate for data-starved hyperspectral image (HSI) restoration. To tackle this problem, this work puts forth a self-supervised diffusion model for HSI restoration, namely Denoising Diffusion Spatio-Spectral Model (DDS2M), which works by inferring the parameters of the proposed Variational Spatio-Spectral Module (VS2M) during the reverse diffusion process, solely using the degraded HSI without any extra training data. In VS2M, a variational inference-based loss function is customized to enable the untrained spatial and spectral networks to learn the posterior distribution, which serves as the transitions of the sampling chain to help reverse the diffusion process. Benefiting from its self-supervised nature and the diffusion process, DDS2M enjoys stronger generalization ability to various HSIs compared to existing diffusion-based methods and superior robustness to noise compared to existing HSI restoration methods. Extensive experiments on HSI denoising, noisy HSI completion and super-resolution on a variety of HSIs demonstrate DDS2M's superiority over the existing task-specific state-of-the-arts.

Denoising diffusion probabilistic models (DDPMs) have been proven capable of synthesizing high-quality images with remarkable diversity when trained on large amounts of data. Typical diffusion models and modern large-scale conditional generative models like text-to-image generative models are vulnerable to overfitting when fine-tuned on extremely limited data. Existing works have explored subject-driven generation using a reference set containing a few images. However, few prior works explore DDPM-based domain-driven generation, which aims to learn the common features of target domains while maintaining diversity. This paper proposes a novel DomainStudio approach to adapt DDPMs pre-trained on large-scale source datasets to target domains using limited data. It is designed to keep the diversity of subjects provided by source domains and get high-quality and diverse adapted samples in target domains. We propose to keep the relative distances between adapted samples to achieve considerable generation diversity. In addition, we further enhance the learning of high-frequency details for better generation quality. Our approach is compatible with both unconditional and conditional diffusion models. This work makes the first attempt to realize unconditional few-shot image generation with diffusion models, achieving better quality and greater diversity than current state-of-the-art GAN-based approaches. Moreover, this work also significantly relieves overfitting for conditional generation and realizes high-quality domain-driven generation, further expanding the applicable scenarios of modern large-scale text-to-image models.

Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on image quality. We enforce the one-step image generator match the diffusion model at distribution level, by minimizing an approximate KL divergence whose gradient can be expressed as the difference between 2 score functions, one of the target distribution and the other of the synthetic distribution being produced by our one-step generator. The score functions are parameterized as two diffusion models trained separately on each distribution. Combined with a simple regression loss matching the large-scale structure of the multi-step diffusion outputs, our method outperforms all published few-step diffusion approaches, reaching 2.62 FID on ImageNet 64x64 and 11.49 FID on zero-shot COCO-30k, comparable to Stable Diffusion but orders of magnitude faster. Utilizing FP16 inference, our model generates images at 20 FPS on modern hardware.

Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that the same noise level on a higher resolution results in a higher Signal-to-Noise Ratio in the frequency domain. In this work, we present Relay Diffusion Model (RDM), which transfers a low-resolution image or noise into an equivalent high-resolution one for diffusion model via blurring diffusion and block noise. Therefore, the diffusion process can continue seamlessly in any new resolution or model without restarting from pure noise or low-resolution conditioning. RDM achieves state-of-the-art FID on CelebA-HQ and sFID on ImageNet 256times256, surpassing previous works such as ADM, LDM and DiT by a large margin. All the codes and checkpoints are open-sourced at https://github.com/THUDM/RelayDiffusion.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

Medical imaging often contains critical fine-grained features, such as tumors or hemorrhages, crucial for diagnosis yet potentially too subtle for detection with conventional methods. In this paper, we introduce DIA, dissolving is amplifying. DIA is a fine-grained anomaly detection framework for medical images. First, we introduce dissolving transformations. We employ diffusion with a generative diffusion model as a dedicated feature-aware denoiser. Applying diffusion to medical images in a certain manner can remove or diminish fine-grained discriminative features. Second, we introduce an amplifying framework based on contrastive learning to learn a semantically meaningful representation of medical images in a self-supervised manner, with a focus on fine-grained features. The amplifying framework contrasts additional pairs of images with and without dissolving transformations applied and thereby emphasizes the dissolved fine-grained features. DIA significantly improves the medical anomaly detection performance with around 18.40\% AUC boost against the baseline method and achieves an overall SOTA against other benchmark methods. Our code is available at https://github.com/shijianjian/DIA.git.

Consistency distillation methods have demonstrated significant success in accelerating generative tasks of diffusion models. However, since previous consistency distillation methods use simple and straightforward strategies in selecting target timesteps, they usually struggle with blurs and detail losses in generated images. To address these limitations, we introduce Target-Driven Distillation (TDD), which (1) adopts a delicate selection strategy of target timesteps, increasing the training efficiency; (2) utilizes decoupled guidances during training, making TDD open to post-tuning on guidance scale during inference periods; (3) can be optionally equipped with non-equidistant sampling and x0 clipping, enabling a more flexible and accurate way for image sampling. Experiments verify that TDD achieves state-of-the-art performance in few-step generation, offering a better choice among consistency distillation models.

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-costly and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results.

Diffusion models have achieved remarkable success across a range of generative tasks. Recent efforts to enhance diffusion model architectures have reimagined them as a form of multi-task learning, where each task corresponds to a denoising task at a specific noise level. While these efforts have focused on parameter isolation and task routing, they fall short of capturing detailed inter-task relationships and risk losing semantic information, respectively. In response, we introduce Switch Diffusion Transformer (Switch-DiT), which establishes inter-task relationships between conflicting tasks without compromising semantic information. To achieve this, we employ a sparse mixture-of-experts within each transformer block to utilize semantic information and facilitate handling conflicts in tasks through parameter isolation. Additionally, we propose a diffusion prior loss, encouraging similar tasks to share their denoising paths while isolating conflicting ones. Through these, each transformer block contains a shared expert across all tasks, where the common and task-specific denoising paths enable the diffusion model to construct its beneficial way of synergizing denoising tasks. Extensive experiments validate the effectiveness of our approach in improving both image quality and convergence rate, and further analysis demonstrates that Switch-DiT constructs tailored denoising paths across various generation scenarios.

Despite all recent progress, it is still challenging to edit and manipulate natural images with modern generative models. When using Generative Adversarial Network (GAN), one major hurdle is in the inversion process mapping a real image to its corresponding noise vector in the latent space, since its necessary to be able to reconstruct an image to edit its contents. Likewise for Denoising Diffusion Implicit Models (DDIM), the linearization assumption in each inversion step makes the whole deterministic inversion process unreliable. Existing approaches that have tackled the problem of inversion stability often incur in significant trade-offs in computational efficiency. In this work we propose an Accelerated Iterative Diffusion Inversion method, dubbed AIDI, that significantly improves reconstruction accuracy with minimal additional overhead in space and time complexity. By using a novel blended guidance technique, we show that effective results can be obtained on a large range of image editing tasks without large classifier-free guidance in inversion. Furthermore, when compared with other diffusion inversion based works, our proposed process is shown to be more robust for fast image editing in the 10 and 20 diffusion steps' regimes.

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds. We provide the code at https://github.com/Daniil-Selikhanovych/ASBM.

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from expensive divergence computation or rely on approximations of heat kernel. These limitations restrict their applicability to simple geometries and hinder scalability to high dimensions. In this work, we introduce the Riemannian Diffusion Mixture, a principled framework for building a generative diffusion process on manifolds. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes derived on general manifolds without requiring heat kernel estimations. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points that guides the process toward the data distribution. We further propose a scalable training objective for learning the mixture process that readily applies to general manifolds. Our method achieves superior performance on diverse manifolds with dramatically reduced number of in-training simulation steps for general manifolds.

While diffusion-based image restoration (IR) methods have achieved remarkable success, they are still limited by the low inference speed attributed to the necessity of executing hundreds or even thousands of sampling steps. Existing acceleration sampling techniques, though seeking to expedite the process, inevitably sacrifice performance to some extent, resulting in over-blurry restored outcomes. To address this issue, this study proposes a novel and efficient diffusion model for IR that significantly reduces the required number of diffusion steps. Our method avoids the need for post-acceleration during inference, thereby avoiding the associated performance deterioration. Specifically, our proposed method establishes a Markov chain that facilitates the transitions between the high-quality and low-quality images by shifting their residuals, substantially improving the transition efficiency. A carefully formulated noise schedule is devised to flexibly control the shifting speed and the noise strength during the diffusion process. Extensive experimental evaluations demonstrate that the proposed method achieves superior or comparable performance to current state-of-the-art methods on three classical IR tasks, namely image super-resolution, image inpainting, and blind face restoration, \textbf{even only with four sampling steps}. Our code and model are publicly available at https://github.com/zsyOAOA/ResShift.

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion model. Achieving faithful inversion remains a challenge, particularly for more recent models trained to generate images with a small number of denoising steps. In this work, we introduce an inversion method with a high quality-to-operation ratio, enhancing reconstruction accuracy without increasing the number of operations. Building on reversing the diffusion sampling process, our method employs an iterative renoising mechanism at each inversion sampling step. This mechanism refines the approximation of a predicted point along the forward diffusion trajectory, by iteratively applying the pretrained diffusion model, and averaging these predictions. We evaluate the performance of our ReNoise technique using various sampling algorithms and models, including recent accelerated diffusion models. Through comprehensive evaluations and comparisons, we show its effectiveness in terms of both accuracy and speed. Furthermore, we confirm that our method preserves editability by demonstrating text-driven image editing on real images.

We introduce Efficient Motion Diffusion Model (EMDM) for fast and high-quality human motion generation. Current state-of-the-art generative diffusion models have produced impressive results but struggle to achieve fast generation without sacrificing quality. On the one hand, previous works, like motion latent diffusion, conduct diffusion within a latent space for efficiency, but learning such a latent space can be a non-trivial effort. On the other hand, accelerating generation by naively increasing the sampling step size, e.g., DDIM, often leads to quality degradation as it fails to approximate the complex denoising distribution. To address these issues, we propose EMDM, which captures the complex distribution during multiple sampling steps in the diffusion model, allowing for much fewer sampling steps and significant acceleration in generation. This is achieved by a conditional denoising diffusion GAN to capture multimodal data distributions among arbitrary (and potentially larger) step sizes conditioned on control signals, enabling fewer-step motion sampling with high fidelity and diversity. To minimize undesired motion artifacts, geometric losses are imposed during network learning. As a result, EMDM achieves real-time motion generation and significantly improves the efficiency of motion diffusion models compared to existing methods while achieving high-quality motion generation. Our code will be publicly available upon publication.

Evaluating the performance of autonomous vehicle planning algorithms necessitates simulating long-tail safety-critical traffic scenarios. However, traditional methods for generating such scenarios often fall short in terms of controllability and realism; they also neglect the dynamics of agent interactions. To address these limitations, we introduce SAFE-SIM, a novel diffusion-based controllable closed-loop safety-critical simulation framework. Our approach yields two distinct advantages: 1) generating realistic long-tail safety-critical scenarios that closely reflect real-world conditions, and 2) providing controllable adversarial behavior for more comprehensive and interactive evaluations. We develop a novel approach to simulate safety-critical scenarios through an adversarial term in the denoising process of diffusion models, which allows an adversarial agent to challenge a planner with plausible maneuvers while all agents in the scene exhibit reactive and realistic behaviors. Furthermore, we propose novel guidance objectives and a partial diffusion process that enables users to control key aspects of the scenarios, such as the collision type and aggressiveness of the adversarial agent, while maintaining the realism of the behavior. We validate our framework empirically using the nuScenes and nuPlan datasets across multiple planners, demonstrating improvements in both realism and controllability. These findings affirm that diffusion models provide a robust and versatile foundation for safety-critical, interactive traffic simulation, extending their utility across the broader autonomous driving landscape. Project website: https://safe-sim.github.io/.

Diffusion probabilistic models (DPMs) have become a popular approach to conditional generation, due to their promising results and support for cross-modal synthesis. A key desideratum in conditional synthesis is to achieve high correspondence between the conditioning input and generated output. Most existing methods learn such relationships implicitly, by incorporating the prior into the variational lower bound. In this work, we take a different route -- we explicitly enhance input-output connections by maximizing their mutual information. To this end, we introduce a Conditional Discrete Contrastive Diffusion (CDCD) loss and design two contrastive diffusion mechanisms to effectively incorporate it into the denoising process, combining the diffusion training and contrastive learning for the first time by connecting it with the conventional variational objectives. We demonstrate the efficacy of our approach in evaluations with diverse multimodal conditional synthesis tasks: dance-to-music generation, text-to-image synthesis, as well as class-conditioned image synthesis. On each, we enhance the input-output correspondence and achieve higher or competitive general synthesis quality. Furthermore, the proposed approach improves the convergence of diffusion models, reducing the number of required diffusion steps by more than 35% on two benchmarks, significantly increasing the inference speed.

Diffusion models have attained remarkable success in the domains of image generation and editing. It is widely recognized that employing larger inversion and denoising steps in diffusion model leads to improved image reconstruction quality. However, the editing performance of diffusion models tends to be no more satisfactory even with increasing denoising steps. The deficiency in editing could be attributed to the conditional Markovian property of the editing process, where errors accumulate throughout denoising steps. To tackle this challenge, we first propose an innovative framework where a rectifier module is incorporated to modulate diffusion model weights with residual features, thereby providing compensatory information to bridge the fidelity gap. Furthermore, we introduce a novel learning paradigm aimed at minimizing error propagation during the editing process, which trains the editing procedure in a manner similar to denoising score-matching. Extensive experiments demonstrate that our proposed framework and training strategy achieve high-fidelity reconstruction and editing results across various levels of denoising steps, meanwhile exhibits exceptional performance in terms of both quantitative metric and qualitative assessments. Moreover, we explore our model's generalization through several applications like image-to-image translation and out-of-domain image editing.

Denoising diffusion probabilistic models (DDPM) have shown remarkable performance in unconditional image generation. However, due to the stochasticity of the generative process in DDPM, it is challenging to generate images with the desired semantics. In this work, we propose Iterative Latent Variable Refinement (ILVR), a method to guide the generative process in DDPM to generate high-quality images based on a given reference image. Here, the refinement of the generative process in DDPM enables a single DDPM to sample images from various sets directed by the reference image. The proposed ILVR method generates high-quality images while controlling the generation. The controllability of our method allows adaptation of a single DDPM without any additional learning in various image generation tasks, such as generation from various downsampling factors, multi-domain image translation, paint-to-image, and editing with scribbles.

Image-based virtual try-on enables users to virtually try on different garments by altering original clothes in their photographs. Generative Adversarial Networks (GANs) dominate the research field in image-based virtual try-on, but have not resolved problems such as unnatural deformation of garments and the blurry generation quality. Recently, diffusion models have emerged with surprising performance across various image generation tasks. While the generative quality of diffusion models is impressive, achieving controllability poses a significant challenge when applying it to virtual try-on tasks and multiple denoising iterations limit its potential for real-time applications. In this paper, we propose Controllable Accelerated virtual Try-on with Diffusion Model called CAT-DM. To enhance the controllability, a basic diffusion-based virtual try-on network is designed, which utilizes ControlNet to introduce additional control conditions and improves the feature extraction of garment images. In terms of acceleration, CAT-DM initiates a reverse denoising process with an implicit distribution generated by a pre-trained GAN-based model. Compared with previous try-on methods based on diffusion models, CAT-DM not only retains the pattern and texture details of the in-shop garment but also reduces the sampling steps without compromising generation quality. Extensive experiments demonstrate the superiority of CAT-DM against both GAN-based and diffusion-based methods in producing more realistic images and accurately reproducing garment patterns. Our code and models will be publicly released.

A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data distribution. Despite its recent success in image synthesis, applying DPMs to video generation is still challenging due to high-dimensional data spaces. Previous methods usually adopt a standard diffusion process, where frames in the same video clip are destroyed with independent noises, ignoring the content redundancy and temporal correlation. This work presents a decomposed diffusion process via resolving the per-frame noise into a base noise that is shared among all frames and a residual noise that varies along the time axis. The denoising pipeline employs two jointly-learned networks to match the noise decomposition accordingly. Experiments on various datasets confirm that our approach, termed as VideoFusion, surpasses both GAN-based and diffusion-based alternatives in high-quality video generation. We further show that our decomposed formulation can benefit from pre-trained image diffusion models and well-support text-conditioned video creation.

Diffusion models have seen rapid adoption in robotic imitation learning, enabling autonomous execution of complex dexterous tasks. However, action synthesis is often slow, requiring many steps of iterative denoising, limiting the extent to which models can be used in tasks that require fast reactive policies. To sidestep this, recent works have explored how the distillation of the diffusion process can be used to accelerate policy synthesis. However, distillation is computationally expensive and can hurt both the accuracy and diversity of synthesized actions. We propose SDP (Streaming Diffusion Policy), an alternative method to accelerate policy synthesis, leveraging the insight that generating a partially denoised action trajectory is substantially faster than a full output action trajectory. At each observation, our approach outputs a partially denoised action trajectory with variable levels of noise corruption, where the immediate action to execute is noise-free, with subsequent actions having increasing levels of noise and uncertainty. The partially denoised action trajectory for a new observation can then be quickly generated by applying a few steps of denoising to the previously predicted noisy action trajectory (rolled over by one timestep). We illustrate the efficacy of this approach, dramatically speeding up policy synthesis while preserving performance across both simulated and real-world settings.

Recent advances in diffusion models have introduced a new era of text-guided image manipulation, enabling users to create realistic edited images with simple textual prompts. However, there is significant concern about the potential misuse of these methods, especially in creating misleading or harmful content. Although recent defense strategies, which introduce imperceptible adversarial noise to induce model failure, have shown promise, they remain ineffective against more sophisticated manipulations, such as editing with a mask. In this work, we propose DiffusionGuard, a robust and effective defense method against unauthorized edits by diffusion-based image editing models, even in challenging setups. Through a detailed analysis of these models, we introduce a novel objective that generates adversarial noise targeting the early stage of the diffusion process. This approach significantly improves the efficiency and effectiveness of adversarial noises. We also introduce a mask-augmentation technique to enhance robustness against various masks during test time. Finally, we introduce a comprehensive benchmark designed to evaluate the effectiveness and robustness of methods in protecting against privacy threats in realistic scenarios. Through extensive experiments, we show that our method achieves stronger protection and improved mask robustness with lower computational costs compared to the strongest baseline. Additionally, our method exhibits superior transferability and better resilience to noise removal techniques compared to all baseline methods. Our source code is publicly available at https://github.com/choi403/DiffusionGuard.

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

Single-view novel view synthesis, the task of generating images from new viewpoints based on a single reference image, is an important but challenging task in computer vision. Recently, Denoising Diffusion Probabilistic Model (DDPM) has become popular in this area due to its strong ability to generate high-fidelity images. However, current diffusion-based methods directly rely on camera pose matrices as viewing conditions, globally and implicitly introducing 3D constraints. These methods may suffer from inconsistency among generated images from different perspectives, especially in regions with intricate textures and structures. In this work, we present Light Field Diffusion (LFD), a conditional diffusion-based model for single-view novel view synthesis. Unlike previous methods that employ camera pose matrices, LFD transforms the camera view information into light field encoding and combines it with the reference image. This design introduces local pixel-wise constraints within the diffusion models, thereby encouraging better multi-view consistency. Experiments on several datasets show that our LFD can efficiently generate high-fidelity images and maintain better 3D consistency even in intricate regions. Our method can generate images with higher quality than NeRF-based models, and we obtain sample quality similar to other diffusion-based models but with only one-third of the model size.

Data attribution seeks to trace model outputs back to training data. With the recent development of diffusion models, data attribution has become a desired module to properly assign valuations for high-quality or copyrighted training samples, ensuring that data contributors are fairly compensated or credited. Several theoretically motivated methods have been proposed to implement data attribution, in an effort to improve the trade-off between computational scalability and effectiveness. In this work, we conduct extensive experiments and ablation studies on attributing diffusion models, specifically focusing on DDPMs trained on CIFAR-10 and CelebA, as well as a Stable Diffusion model LoRA-finetuned on ArtBench. Intriguingly, we report counter-intuitive observations that theoretically unjustified design choices for attribution empirically outperform previous baselines by a large margin, in terms of both linear datamodeling score and counterfactual evaluation. Our work presents a significantly more efficient approach for attributing diffusion models, while the unexpected findings suggest that at least in non-convex settings, constructions guided by theoretical assumptions may lead to inferior attribution performance. The code is available at https://github.com/sail-sg/D-TRAK.

Denoising diffusion models have shown great promise in human motion synthesis conditioned on natural language descriptions. However, integrating spatial constraints, such as pre-defined motion trajectories and obstacles, remains a challenge despite being essential for bridging the gap between isolated human motion and its surrounding environment. To address this issue, we propose Guided Motion Diffusion (GMD), a method that incorporates spatial constraints into the motion generation process. Specifically, we propose an effective feature projection scheme that manipulates motion representation to enhance the coherency between spatial information and local poses. Together with a new imputation formulation, the generated motion can reliably conform to spatial constraints such as global motion trajectories. Furthermore, given sparse spatial constraints (e.g. sparse keyframes), we introduce a new dense guidance approach to turn a sparse signal, which is susceptible to being ignored during the reverse steps, into denser signals to guide the generated motion to the given constraints. Our extensive experiments justify the development of GMD, which achieves a significant improvement over state-of-the-art methods in text-based motion generation while allowing control of the synthesized motions with spatial constraints.

While generative diffusion models excel in producing high-quality images, they can also be misused to mimic authorized images, posing a significant threat to AI systems. Efforts have been made to add calibrated perturbations to protect images from diffusion-based mimicry pipelines. However, most of the existing methods are too ineffective and even impractical to be used by individual users due to their high computation and memory requirements. In this work, we present novel findings on attacking latent diffusion models (LDM) and propose new plug-and-play strategies for more effective protection. In particular, we explore the bottleneck in attacking an LDM, discovering that the encoder module rather than the denoiser module is the vulnerable point. Based on this insight, we present our strategy using Score Distillation Sampling (SDS) to double the speed of protection and reduce memory occupation by half without compromising its strength. Additionally, we provide a robust protection strategy by counterintuitively minimizing the semantic loss, which can assist in generating more natural perturbations. Finally, we conduct extensive experiments to substantiate our findings and comprehensively evaluate our newly proposed strategies. We hope our insights and protective measures can contribute to better defense against malicious diffusion-based mimicry, advancing the development of secure AI systems. The code is available in https://github.com/xavihart/Diff-Protect

Human motion modeling is important for many modern graphics applications, which typically require professional skills. In order to remove the skill barriers for laymen, recent motion generation methods can directly generate human motions conditioned on natural languages. However, it remains challenging to achieve diverse and fine-grained motion generation with various text inputs. To address this problem, we propose MotionDiffuse, the first diffusion model-based text-driven motion generation framework, which demonstrates several desired properties over existing methods. 1) Probabilistic Mapping. Instead of a deterministic language-motion mapping, MotionDiffuse generates motions through a series of denoising steps in which variations are injected. 2) Realistic Synthesis. MotionDiffuse excels at modeling complicated data distribution and generating vivid motion sequences. 3) Multi-Level Manipulation. MotionDiffuse responds to fine-grained instructions on body parts, and arbitrary-length motion synthesis with time-varied text prompts. Our experiments show MotionDiffuse outperforms existing SoTA methods by convincing margins on text-driven motion generation and action-conditioned motion generation. A qualitative analysis further demonstrates MotionDiffuse's controllability for comprehensive motion generation. Homepage: https://mingyuan-zhang.github.io/projects/MotionDiffuse.html

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic differential equations (SDEs) and ordinary differential equations (ODEs). Empirically, it has been reported that ODE based samples are inferior to SDE based samples. In this paper we rigorously describe the range of dynamics and approximations that arise when training score-based diffusion models, including the true SDE dynamics, the neural approximations, the various approximate particle dynamics that result, as well as their associated Fokker--Planck equations and the neural network approximations of these Fokker--Planck equations. We systematically analyse the difference between the ODE and SDE dynamics of score-based diffusion models, and link it to an associated Fokker--Planck equation. We derive a theoretical upper bound on the Wasserstein 2-distance between the ODE- and SDE-induced distributions in terms of a Fokker--Planck residual. We also show numerically that conventional score-based diffusion models can exhibit significant differences between ODE- and SDE-induced distributions which we demonstrate using explicit comparisons. Moreover, we show numerically that reducing the Fokker--Planck residual by adding it as an additional regularisation term leads to closing the gap between ODE- and SDE-induced distributions. Our experiments suggest that this regularisation can improve the distribution generated by the ODE, however that this can come at the cost of degraded SDE sample quality.

The integration of Vector Quantised Variational AutoEncoder (VQ-VAE) with autoregressive models as generation part has yielded high-quality results on image generation. However, the autoregressive models will strictly follow the progressive scanning order during the sampling phase. This leads the existing VQ series models to hardly escape the trap of lacking global information. Denoising Diffusion Probabilistic Models (DDPM) in the continuous domain have shown a capability to capture the global context, while generating high-quality images. In the discrete state space, some works have demonstrated the potential to perform text generation and low resolution image generation. We show that with the help of a content-rich discrete visual codebook from VQ-VAE, the discrete diffusion model can also generate high fidelity images with global context, which compensates for the deficiency of the classical autoregressive model along pixel space. Meanwhile, the integration of the discrete VAE with the diffusion model resolves the drawback of conventional autoregressive models being oversized, and the diffusion model which demands excessive time in the sampling process when generating images. It is found that the quality of the generated images is heavily dependent on the discrete visual codebook. Extensive experiments demonstrate that the proposed Vector Quantised Discrete Diffusion Model (VQ-DDM) is able to achieve comparable performance to top-tier methods with low complexity. It also demonstrates outstanding advantages over other vectors quantised with autoregressive models in terms of image inpainting tasks without additional training.

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 16s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.

We present a unified probabilistic formulation for diffusion-based image editing, where a latent variable is edited in a task-specific manner and generally deviates from the corresponding marginal distribution induced by the original stochastic or ordinary differential equation (SDE or ODE). Instead, it defines a corresponding SDE or ODE for editing. In the formulation, we prove that the Kullback-Leibler divergence between the marginal distributions of the two SDEs gradually decreases while that for the ODEs remains as the time approaches zero, which shows the promise of SDE in image editing. Inspired by it, we provide the SDE counterparts for widely used ODE baselines in various tasks including inpainting and image-to-image translation, where SDE shows a consistent and substantial improvement. Moreover, we propose SDE-Drag -- a simple yet effective method built upon the SDE formulation for point-based content dragging. We build a challenging benchmark (termed DragBench) with open-set natural, art, and AI-generated images for evaluation. A user study on DragBench indicates that SDE-Drag significantly outperforms our ODE baseline, existing diffusion-based methods, and the renowned DragGAN. Our results demonstrate the superiority and versatility of SDE in image editing and push the boundary of diffusion-based editing methods.

Super-resolution methods are increasingly becoming popular for both real-world and face-specific tasks. Many existing approaches, however, rely on simplistic degradation models, which limits their ability to handle complex and unknown degradation patterns effectively. While diffusion-based super-resolution techniques have recently shown impressive results, they are still constrained by the need for numerous inference steps. To address this, we propose TDDSR, an efficient single-step diffusion-based super-resolution method. Our method, distilled from a pre-trained teacher model and based on a diffusion network, performs super-resolution in a single step. It integrates a learnable diffusion-based downsampler to capture diverse degradation patterns and employs two discriminators, one for high-resolution and one for low-resolution images, to enhance the overall performance. Experimental results demonstrate its effectiveness across real-world and face-specific SR tasks, achieving performance beyond other state-of-the-art models and comparable to previous diffusion methods with multiple sampling steps.

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.

In this study, we examine the representation learning abilities of Denoising Diffusion Models (DDM) that were originally purposed for image generation. Our philosophy is to deconstruct a DDM, gradually transforming it into a classical Denoising Autoencoder (DAE). This deconstructive procedure allows us to explore how various components of modern DDMs influence self-supervised representation learning. We observe that only a very few modern components are critical for learning good representations, while many others are nonessential. Our study ultimately arrives at an approach that is highly simplified and to a large extent resembles a classical DAE. We hope our study will rekindle interest in a family of classical methods within the realm of modern self-supervised learning.

Denoising diffusion probabilistic models that were initially proposed for realistic image generation have recently shown success in various perception tasks (e.g., object detection and image segmentation) and are increasingly gaining attention in computer vision. However, extending such models to multi-frame human pose estimation is non-trivial due to the presence of the additional temporal dimension in videos. More importantly, learning representations that focus on keypoint regions is crucial for accurate localization of human joints. Nevertheless, the adaptation of the diffusion-based methods remains unclear on how to achieve such objective. In this paper, we present DiffPose, a novel diffusion architecture that formulates video-based human pose estimation as a conditional heatmap generation problem. First, to better leverage temporal information, we propose SpatioTemporal Representation Learner which aggregates visual evidences across frames and uses the resulting features in each denoising step as a condition. In addition, we present a mechanism called Lookup-based MultiScale Feature Interaction that determines the correlations between local joints and global contexts across multiple scales. This mechanism generates delicate representations that focus on keypoint regions. Altogether, by extending diffusion models, we show two unique characteristics from DiffPose on pose estimation task: (i) the ability to combine multiple sets of pose estimates to improve prediction accuracy, particularly for challenging joints, and (ii) the ability to adjust the number of iterative steps for feature refinement without retraining the model. DiffPose sets new state-of-the-art results on three benchmarks: PoseTrack2017, PoseTrack2018, and PoseTrack21.

Most existing Image Restoration (IR) models are task-specific, which can not be generalized to different degradation operators. In this work, we propose the Denoising Diffusion Null-Space Model (DDNM), a novel zero-shot framework for arbitrary linear IR problems, including but not limited to image super-resolution, colorization, inpainting, compressed sensing, and deblurring. DDNM only needs a pre-trained off-the-shelf diffusion model as the generative prior, without any extra training or network modifications. By refining only the null-space contents during the reverse diffusion process, we can yield diverse results satisfying both data consistency and realness. We further propose an enhanced and robust version, dubbed DDNM+, to support noisy restoration and improve restoration quality for hard tasks. Our experiments on several IR tasks reveal that DDNM outperforms other state-of-the-art zero-shot IR methods. We also demonstrate that DDNM+ can solve complex real-world applications, e.g., old photo restoration.

We introduce Animate124 (Animate-one-image-to-4D), the first work to animate a single in-the-wild image into 3D video through textual motion descriptions, an underexplored problem with significant applications. Our 4D generation leverages an advanced 4D grid dynamic Neural Radiance Field (NeRF) model, optimized in three distinct stages using multiple diffusion priors. Initially, a static model is optimized using the reference image, guided by 2D and 3D diffusion priors, which serves as the initialization for the dynamic NeRF. Subsequently, a video diffusion model is employed to learn the motion specific to the subject. However, the object in the 3D videos tends to drift away from the reference image over time. This drift is mainly due to the misalignment between the text prompt and the reference image in the video diffusion model. In the final stage, a personalized diffusion prior is therefore utilized to address the semantic drift. As the pioneering image-text-to-4D generation framework, our method demonstrates significant advancements over existing baselines, evidenced by comprehensive quantitative and qualitative assessments.

Diffusion models have recently shown significant potential in solving decision-making problems, particularly in generating behavior plans -- also known as diffusion planning. While numerous studies have demonstrated the impressive performance of diffusion planning, the mechanisms behind the key components of a good diffusion planner remain unclear and the design choices are highly inconsistent in existing studies. In this work, we address this issue through systematic empirical experiments on diffusion planning in an offline reinforcement learning (RL) setting, providing practical insights into the essential components of diffusion planning. We trained and evaluated over 6,000 diffusion models, identifying the critical components such as guided sampling, network architecture, action generation and planning strategy. We revealed that some design choices opposite to the common practice in previous work in diffusion planning actually lead to better performance, e.g., unconditional sampling with selection can be better than guided sampling and Transformer outperforms U-Net as denoising network. Based on these insights, we suggest a simple yet strong diffusion planning baseline that achieves state-of-the-art results on standard offline RL benchmarks.

Diffusion models have demonstrated impressive generative capabilities, but their exposure bias problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at https://github.com/forever208/ADM-ES and https://github.com/forever208/EDM-ES.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate O(1/{T}^2) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate O(1/T), outperforming the rate O(1/T) for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates ell_2-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

Data is the cornerstone of deep learning. This paper reveals that the recently developed Diffusion Model is a scalable data engine for object detection. Existing methods for scaling up detection-oriented data often require manual collection or generative models to obtain target images, followed by data augmentation and labeling to produce training pairs, which are costly, complex, or lacking diversity. To address these issues, we presentDiffusionEngine (DE), a data scaling-up engine that provides high-quality detection-oriented training pairs in a single stage. DE consists of a pre-trained diffusion model and an effective Detection-Adapter, contributing to generating scalable, diverse and generalizable detection data in a plug-and-play manner. Detection-Adapter is learned to align the implicit semantic and location knowledge in off-the-shelf diffusion models with detection-aware signals to make better bounding-box predictions. Additionally, we contribute two datasets, i.e., COCO-DE and VOC-DE, to scale up existing detection benchmarks for facilitating follow-up research. Extensive experiments demonstrate that data scaling-up via DE can achieve significant improvements in diverse scenarios, such as various detection algorithms, self-supervised pre-training, data-sparse, label-scarce, cross-domain, and semi-supervised learning. For example, when using DE with a DINO-based adapter to scale up data, mAP is improved by 3.1% on COCO, 7.6% on VOC, and 11.5% on Clipart.

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled generation in general. In this work we introduce D-Flow, a simple framework for controlling the generation process by differentiating through the flow, optimizing for the source (noise) point. We motivate this framework by our key observation stating that for Diffusion/FM models trained with Gaussian probability paths, differentiating through the generation process projects gradient on the data manifold, implicitly injecting the prior into the optimization process. We validate our framework on linear and non-linear controlled generation problems including: image and audio inverse problems and conditional molecule generation reaching state of the art performance across all.

Interactive motion synthesis is essential in creating immersive experiences in entertainment applications, such as video games and virtual reality. However, generating animations that are both high-quality and contextually responsive remains a challenge. Traditional techniques in the game industry can produce high-fidelity animations but suffer from high computational costs and poor scalability. Trained neural network models alleviate the memory and speed issues, yet fall short on generating diverse motions. Diffusion models offer diverse motion synthesis with low memory usage, but require expensive reverse diffusion processes. This paper introduces the Accelerated Auto-regressive Motion Diffusion Model (AAMDM), a novel motion synthesis framework designed to achieve quality, diversity, and efficiency all together. AAMDM integrates Denoising Diffusion GANs as a fast Generation Module, and an Auto-regressive Diffusion Model as a Polishing Module. Furthermore, AAMDM operates in a lower-dimensional embedded space rather than the full-dimensional pose space, which reduces the training complexity as well as further improves the performance. We show that AAMDM outperforms existing methods in motion quality, diversity, and runtime efficiency, through comprehensive quantitative analyses and visual comparisons. We also demonstrate the effectiveness of each algorithmic component through ablation studies.

While methods for monocular depth estimation have made significant strides on standard benchmarks, zero-shot metric depth estimation remains unsolved. Challenges include the joint modeling of indoor and outdoor scenes, which often exhibit significantly different distributions of RGB and depth, and the depth-scale ambiguity due to unknown camera intrinsics. Recent work has proposed specialized multi-head architectures for jointly modeling indoor and outdoor scenes. In contrast, we advocate a generic, task-agnostic diffusion model, with several advancements such as log-scale depth parameterization to enable joint modeling of indoor and outdoor scenes, conditioning on the field-of-view (FOV) to handle scale ambiguity and synthetically augmenting FOV during training to generalize beyond the limited camera intrinsics in training datasets. Furthermore, by employing a more diverse training mixture than is common, and an efficient diffusion parameterization, our method, DMD (Diffusion for Metric Depth) achieves a 25\% reduction in relative error (REL) on zero-shot indoor and 33\% reduction on zero-shot outdoor datasets over the current SOTA using only a small number of denoising steps. For an overview see https://diffusion-vision.github.io/dmd

Drawing upon recent advances in language model alignment, we formulate offline Reinforcement Learning as a two-stage optimization problem: First pretraining expressive generative policies on reward-free behavior datasets, then fine-tuning these policies to align with task-specific annotations like Q-values. This strategy allows us to leverage abundant and diverse behavior data to enhance generalization and enable rapid adaptation to downstream tasks using minimal annotations. In particular, we introduce Efficient Diffusion Alignment (EDA) for solving continuous control problems. EDA utilizes diffusion models for behavior modeling. However, unlike previous approaches, we represent diffusion policies as the derivative of a scalar neural network with respect to action inputs. This representation is critical because it enables direct density calculation for diffusion models, making them compatible with existing LLM alignment theories. During policy fine-tuning, we extend preference-based alignment methods like Direct Preference Optimization (DPO) to align diffusion behaviors with continuous Q-functions. Our evaluation on the D4RL benchmark shows that EDA exceeds all baseline methods in overall performance. Notably, EDA maintains about 95\% of performance and still outperforms several baselines given only 1\% of Q-labelled data during fine-tuning.

Diffusion models have demonstrated remarkable capabilities in image generation tasks, including image editing and video creation, representing a good understanding of the physical world. On the other line, diffusion models have also shown promise in robotic control tasks by denoising actions, known as diffusion policy. Although the diffusion generative model and diffusion policy exhibit distinct capabilities--image prediction and robotic action, respectively--they technically follow a similar denoising process. In robotic tasks, the ability to predict future images and generate actions is highly correlated since they share the same underlying dynamics of the physical world. Building on this insight, we introduce PAD, a novel visual policy learning framework that unifies image Prediction and robot Action within a joint Denoising process. Specifically, PAD utilizes Diffusion Transformers (DiT) to seamlessly integrate images and robot states, enabling the simultaneous prediction of future images and robot actions. Additionally, PAD supports co-training on both robotic demonstrations and large-scale video datasets and can be easily extended to other robotic modalities, such as depth images. PAD outperforms previous methods, achieving a significant 26.3% relative improvement on the full Metaworld benchmark, by utilizing a single text-conditioned visual policy within a data-efficient imitation learning setting. Furthermore, PAD demonstrates superior generalization to unseen tasks in real-world robot manipulation settings with 28.0% success rate increase compared to the strongest baseline. Project page at https://sites.google.com/view/pad-paper

A diffusion model, which is formulated to produce an image using thousands of denoising steps, usually suffers from a slow inference speed. Existing acceleration algorithms simplify the sampling by skipping most steps yet exhibit considerable performance degradation. By viewing the generation of diffusion models as a discretized integrating process, we argue that the quality drop is partly caused by applying an inaccurate integral direction to a timestep interval. To rectify this issue, we propose a timestep aligner that helps find a more accurate integral direction for a particular interval at the minimum cost. Specifically, at each denoising step, we replace the original parameterization by conditioning the network on a new timestep, which is obtained by aligning the sampling distribution to the real distribution. Extensive experiments show that our plug-in design can be trained efficiently and boost the inference performance of various state-of-the-art acceleration methods, especially when there are few denoising steps. For example, when using 10 denoising steps on the popular LSUN Bedroom dataset, we improve the FID of DDIM from 9.65 to 6.07, simply by adopting our method for a more appropriate set of timesteps. Code will be made publicly available.

Nine-degrees-of-freedom (9-DoF) object pose and size estimation is crucial for enabling augmented reality and robotic manipulation. Category-level methods have received extensive research attention due to their potential for generalization to intra-class unknown objects. However, these methods require manual collection and labeling of large-scale real-world training data. To address this problem, we introduce a diffusion-based paradigm for domain-generalized category-level 9-DoF object pose estimation. Our motivation is to leverage the latent generalization ability of the diffusion model to address the domain generalization challenge in object pose estimation. This entails training the model exclusively on rendered synthetic data to achieve generalization to real-world scenes. We propose an effective diffusion model to redefine 9-DoF object pose estimation from a generative perspective. Our model does not require any 3D shape priors during training or inference. By employing the Denoising Diffusion Implicit Model, we demonstrate that the reverse diffusion process can be executed in as few as 3 steps, achieving near real-time performance. Finally, we design a robotic grasping system comprising both hardware and software components. Through comprehensive experiments on two benchmark datasets and the real-world robotic system, we show that our method achieves state-of-the-art domain generalization performance. Our code will be made public at https://github.com/CNJianLiu/Diff9D.

Diffusion models are the current state-of-the-art in image generation, synthesizing high-quality images by breaking down the generation process into many fine-grained denoising steps. Despite their good performance, diffusion models are computationally expensive, requiring many neural function evaluations (NFEs). In this work, we propose an anytime diffusion-based method that can generate viable images when stopped at arbitrary times before completion. Using existing pretrained diffusion models, we show that the generation scheme can be recomposed as two nested diffusion processes, enabling fast iterative refinement of a generated image. We use this Nested Diffusion approach to peek into the generation process and enable flexible scheduling based on the instantaneous preference of the user. In experiments on ImageNet and Stable Diffusion-based text-to-image generation, we show, both qualitatively and quantitatively, that our method's intermediate generation quality greatly exceeds that of the original diffusion model, while the final slow generation result remains comparable.

Recent inverse problem solvers that leverage generative diffusion priors have garnered significant attention due to their exceptional quality. However, adaptation of the prior is necessary when there exists a discrepancy between the training and testing distributions. In this work, we propose deep diffusion image prior (DDIP), which generalizes the recent adaptation method of SCD by introducing a formal connection to the deep image prior. Under this framework, we propose an efficient adaptation method dubbed D3IP, specified for 3D measurements, which accelerates DDIP by orders of magnitude while achieving superior performance. D3IP enables seamless integration of 3D inverse solvers and thus leads to coherent 3D reconstruction. Moreover, we show that meta-learning techniques can also be applied to yield even better performance. We show that our method is capable of solving diverse 3D reconstructive tasks from the generative prior trained only with phantom images that are vastly different from the training set, opening up new opportunities of applying diffusion inverse solvers even when training with gold standard data is impossible. Code: https://github.com/HJ-harry/DDIP3D

Imitation Learning presents a promising approach for learning generalizable and complex robotic skills. The recently proposed Diffusion Policy generates robot action sequences through a conditional denoising diffusion process, achieving state-of-the-art performance compared to other imitation learning methods. This paper summarizes five key components of Diffusion Policy: 1) observation sequence input; 2) action sequence execution; 3) receding horizon; 4) U-Net or Transformer network architecture; and 5) FiLM conditioning. By conducting experiments across ManiSkill and Adroit benchmarks, this study aims to elucidate the contribution of each component to the success of Diffusion Policy in various scenarios. We hope our findings will provide valuable insights for the application of Diffusion Policy in future research and industry.

Guidance is a crucial technique for extracting the best performance out of image-generating diffusion models. Traditionally, a constant guidance weight has been applied throughout the sampling chain of an image. We show that guidance is clearly harmful toward the beginning of the chain (high noise levels), largely unnecessary toward the end (low noise levels), and only beneficial in the middle. We thus restrict it to a specific range of noise levels, improving both the inference speed and result quality. This limited guidance interval improves the record FID in ImageNet-512 significantly, from 1.81 to 1.40. We show that it is quantitatively and qualitatively beneficial across different sampler parameters, network architectures, and datasets, including the large-scale setting of Stable Diffusion XL. We thus suggest exposing the guidance interval as a hyperparameter in all diffusion models that use guidance.

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.

Millimeter wave (mmWave) radars have attracted significant attention from both academia and industry due to their capability to operate in extreme weather conditions. However, they face challenges in terms of sparsity and noise interference, which hinder their application in the field of micro aerial vehicle (MAV) autonomous navigation. To this end, this paper proposes a novel approach to dense and accurate mmWave radar point cloud construction via cross-modal learning. Specifically, we introduce diffusion models, which possess state-of-the-art performance in generative modeling, to predict LiDAR-like point clouds from paired raw radar data. We also incorporate the most recent diffusion model inference accelerating techniques to ensure that the proposed method can be implemented on MAVs with limited computing resources.We validate the proposed method through extensive benchmark comparisons and real-world experiments, demonstrating its superior performance and generalization ability. Code and pretrained models will be available at https://github.com/ZJU-FAST-Lab/Radar-Diffusion.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Real-world image super-resolution (Real-ISR) aims to reconstruct high-resolution images from low-resolution inputs degraded by complex, unknown processes. While many Stable Diffusion (SD)-based Real-ISR methods have achieved remarkable success, their slow, multi-step inference hinders practical deployment. Recent SD-based one-step networks like OSEDiff and S3Diff alleviate this issue but still incur high computational costs due to their reliance on large pretrained SD models. This paper proposes a novel Real-ISR method, AdcSR, by distilling the one-step diffusion network OSEDiff into a streamlined diffusion-GAN model under our Adversarial Diffusion Compression (ADC) framework. We meticulously examine the modules of OSEDiff, categorizing them into two types: (1) Removable (VAE encoder, prompt extractor, text encoder, etc.) and (2) Prunable (denoising UNet and VAE decoder). Since direct removal and pruning can degrade the model's generation capability, we pretrain our pruned VAE decoder to restore its ability to decode images and employ adversarial distillation to compensate for performance loss. This ADC-based diffusion-GAN hybrid design effectively reduces complexity by 73% in inference time, 78% in computation, and 74% in parameters, while preserving the model's generation capability. Experiments manifest that our proposed AdcSR achieves competitive recovery quality on both synthetic and real-world datasets, offering up to 9.3times speedup over previous one-step diffusion-based methods. Code and models are available at https://github.com/Guaishou74851/AdcSR.

Synthetic Aperture Radar (SAR) provides all-weather, high-resolution imaging capabilities, but its unique imaging mechanism often requires expert interpretation, limiting its widespread applicability. Translating SAR images into more easily recognizable optical images using diffusion models helps address this challenge. However, diffusion models suffer from high latency due to numerous iterative inferences, while Generative Adversarial Networks (GANs) can achieve image translation with just a single iteration but often at the cost of image quality. To overcome these issues, we propose a new training framework for SAR-to-optical image translation that combines the strengths of both approaches. Our method employs consistency distillation to reduce iterative inference steps and integrates adversarial learning to ensure image clarity and minimize color shifts. Additionally, our approach allows for a trade-off between quality and speed, providing flexibility based on application requirements. We conducted experiments on SEN12 and GF3 datasets, performing quantitative evaluations using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Frechet Inception Distance (FID), as well as calculating the inference latency. The results demonstrate that our approach significantly improves inference speed by 131 times while maintaining the visual quality of the generated images, thus offering a robust and efficient solution for SAR-to-optical image translation.

Recently, the diffusion model has emerged as a powerful generative technique for robotic policy learning, capable of modeling multi-mode action distributions. Leveraging its capability for end-to-end autonomous driving is a promising direction. However, the numerous denoising steps in the robotic diffusion policy and the more dynamic, open-world nature of traffic scenes pose substantial challenges for generating diverse driving actions at a real-time speed. To address these challenges, we propose a novel truncated diffusion policy that incorporates prior multi-mode anchors and truncates the diffusion schedule, enabling the model to learn denoising from anchored Gaussian distribution to the multi-mode driving action distribution. Additionally, we design an efficient cascade diffusion decoder for enhanced interaction with conditional scene context. The proposed model, DiffusionDrive, demonstrates 10times reduction in denoising steps compared to vanilla diffusion policy, delivering superior diversity and quality in just 2 steps. On the planning-oriented NAVSIM dataset, with the aligned ResNet-34 backbone, DiffusionDrive achieves 88.1 PDMS without bells and whistles, setting a new record, while running at a real-time speed of 45 FPS on an NVIDIA 4090. Qualitative results on challenging scenarios further confirm that DiffusionDrive can robustly generate diverse plausible driving actions. Code and model will be available at https://github.com/hustvl/DiffusionDrive.