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Physics-Informed Video Diffusion for Shallow Water Equations

MCML Authors

Abstract

Traditional fluid dynamics simulation pipelines combine numerical solvers with rendering, producing highly realistic results but at considerable computational cost. Diffusion-based generative video models offer a faster alternative, yet often ignore physical laws and thus fail to capture consistent dynamics. We propose a physics-informed video diffusion framework that jointly generates visual outputs and physical states. Unlike prior two-stage approaches that first simulate the physical variables and then render, we directly integrate physics constraints into the generative process, enabling simultaneous prediction of physical states and realistic videos without a separate rendering step. Built on the two-dimensional shallow water equations with terrain topography, our method produces temporally coherent water flow while maintaining physical plausibility. Experiments show that it outperforms purely data-driven video diffusion baselines in both realism and physical fidelity, while generating videos significantly faster than traditional simulation-plus-rendering pipelines.

inproceedings BEL+26

ICASSP 2026

IEEE International Conference on Acoustics, Speech and Signal Processing. Barcelona, Spain, May 04-08, 2026.

Authors

Y. Bai • G. Eskandar • Z. Liu • G. Kutyniok

Links

DOI

Research Area

 A2 | Mathematical Foundations

BibTeXKey: BEL+26

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