Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation

Generative models have significantly influenced both vision and language domains, ushering in innovative multimodal applications. Although these achievements have motivated exploration in scientific and engineering fields, challenges emerge, particularly in constrained settings with limited data where precision is crucial. Traditional engineering optimization methods rooted in physics often surpass generative models in these contexts. 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 trajectory derived from physics-based iterative optimization methods. This alignment ensures that the sampling process remains grounded in the underlying physical principles. This alignment eliminates the need for costly preprocessing, external surrogate models, or extra labeled data, generating feasible and high-performance designs efficiently. 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. DOM's efficiency and performance improvements significantly expedite design processes and steer them toward optimal and manufacturable outcomes, highlighting the potential of generative models in data-driven design.