Efficient Physics-Constrained Diffusion Models for Solving Inverse Problems

Seungjun Lee, Shinjae Yoo

Keywords: physics-constraints inverse problem, diffusion model, PDE, generative modeling

TL;DR: We propose a novel framework for solving physics-constrained inverse problems by integrating physics constraints and diffusion models.

Abstract:

Solving inverse problems in scientific and engineering domains often involves complex, nonlinear forward physics and ill-posed conditions.
Recent advancements in diffusion model have shown promise for general inverse problems, yet their application to scientific domains remains less explored and is hindered by the complexity and high non-linearity of physics constraints. We present a physics-constrained diffusion model (PCDM) designed to solve inverse problems in scientific and engineering domains by efficiently integrating pre-trained diffusion models and physics-constrained objectives.
We leverage accelerated diffusion sampling to enable a practical generation process while strictly adhering to physics constraints by solving optimization problems at each timestep. By decoupling the likelihood optimization from the reverse diffusion steps, we ensure that the solutions remain physically consistent, even when employing fewer sampling steps.
We validate our method on a wide range of challenging physics-constrained inverse problems, including data assimilation, topology optimization, and full-waveform inversion. Experimental results show that our approach significantly outperforms existing methods in efficiency and precision, making it practical for real-world applications.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 12020