Constrained Synthesis with Projected Diffusion Models
This addresses the challenge of ensuring constraint satisfaction in generative models for domains like materials science and robotics, representing an incremental improvement by extending diffusion models with optimization-based steering.
The paper tackles the problem of making generative diffusion models comply with constraints and physical principles by reformulating sampling as a constrained optimization problem, enabling applications such as material synthesis with precise properties and physics-informed motion generation.
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints. These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.