ICML 2026poster0 citations
Particle-Guided Diffusion Models for Partial Differential Equations
Andrew Millard, Fredrik Lindsten, Zheng Zhao
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.
DiffusionBenchmark
BibTeX
@inproceedings{
millard2026particleguided,
title={Particle-Guided Diffusion Models for Partial Differential Equations},
author={Andrew Millard and Fredrik Lindsten and Zheng Zhao},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=tX1k4GQtLC}
}