Aligning Optimization Trajectories with Diffusion Models for Constrained
  Design Generation
Giorgio Giannone Akash Srivastava Ole Winther Faez Ahmed
Generative models have had a profound impact on vision and language, paving
the way for a new era of multimodal generative applications. While these
successes have inspired researchers to explore using generative models in
science and engineering to accelerate the design process and reduce the
reliance on iterative optimization, challenges remain. Specifically,
engineering optimization methods based on physics still outperform generative
models when dealing with constrained environments where data is scarce and
precision is paramount. To address these challenges, we introduce Diffusion
Optimization Models (DOM) and Trajectory Alignment (TA), a learning framework
that demonstrates the efficacy of aligning the sampling trajectory of diffusion
models with the optimization trajectory derived from traditional physics-based
methods. This alignment ensures that the sampling process remains grounded in
the underlying physical principles. Our method allows for generating feasible
and high-performance designs in as few as two steps without the need for
expensive preprocessing, external surrogate models, or additional labeled data.
We apply our framework to structural topology optimization, a fundamental
problem in mechanical design, evaluating its performance on in- and
out-of-distribution configurations. Our results demonstrate that TA outperforms
state-of-the-art deep generative models on in-distribution configurations and
halves the inference computational cost. When coupled with a few steps of
optimization, it also improves manufacturability for out-of-distribution
conditions. By significantly improving performance and inference efficiency,
DOM enables us to generate high-quality designs in just a few steps and guide
them toward regions of high performance and manufacturability, paving the way
for the widespread application of generative models in large-scale data-driven
design.