Particle-Guided Diffusion Models for Partial Differential Equations

2026/01/30 by Andrew Millard, Fredrik Lindsten, Zheng Zhao · 1 voice · 4 citations
Computer Science · #cs.LG

paper · pdf · doi:10.48550/arxiv.2601.23262

arxiv published 2026/01/30 · arxiv updated 2026/05/27

Abstract

We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical error than existing state-of-the-art generative methods.

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Discussions

• Physics and AI, usually at odds, find a new harmony in particle-guided diffusion models. It’s a subtle shift: solutions that honor both creativity and physical laws. Could this approach unlock new pos [bsky, 0 points, 0 comments]

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