Exploring Straighter Trajectories of Flow Matching with Diffusion
  Guidance
Siyu Xing Jie Cao Huaibo Huang Xiao-Yu Zhang Ran He
Flow matching as a paradigm of generative model achieves notable success
across various domains. However, existing methods use either multi-round
training or knowledge within minibatches, posing challenges in finding a
favorable coupling strategy for straight trajectories. To address this issue,
we propose a novel approach, Straighter trajectories of Flow Matching
(StraightFM). It straightens trajectories with the coupling strategy guided by
diffusion model from entire distribution level. First, we propose a coupling
strategy to straighten trajectories, creating couplings between image and noise
samples under diffusion model guidance. Second, StraightFM also integrates real
data to enhance training, employing a neural network to parameterize another
coupling process from images to noise samples. StraightFM is jointly optimized
with couplings from above two mutually complementary directions, resulting in
straighter trajectories and enabling both one-step and few-step generation.
Extensive experiments demonstrate that StraightFM yields high quality samples
with fewer step. StraightFM generates visually appealing images with a lower
FID among diffusion and traditional flow matching methods within 5 sampling
steps when trained on pixel space. In the latent space (i.e., Latent
Diffusion), StraightFM achieves a lower KID value compared to existing methods
on the CelebA-HQ 256 dataset in fewer than 10 sampling steps.