Physics-Informed Conditional Diffusion for Multi-Modal PDEs

Summary

We propose a mesh-free physics-informed conditional diffusion framework for multi-modal PDEs, including quantum systems (Schrödinger), wave propagation (Helmholtz) and nonlinear dynamics (Gross-Pitaevskii). Training combines a physics loss with a data loss and samples with DDIM. Against baselines, it reduces MSE by 13% and Wasserstein-1 distance by 10%, and avoids mode collapse across 1D and 2D PDE domains.

OpenReview

Citation

@inproceedings{
garg2026physicsinformed,
title={Physics-Informed Conditional Diffusion for Multi-Modal {PDE}s},
author={Tanmay Garg and Thanh Ngoc Pham and Barnabas Poczos and Aarti Singh},
booktitle={AI{\&}PDE: ICLR 2026 Workshop on AI and Partial Differential Equations},
year={2026},
url={https://openreview.net/forum?id=7OwjPIfFza}
}