Physics-Informed Video Diffusion For Shallow Water Equations

TL;DR

This paper introduces a physics-informed video diffusion model that jointly generates realistic videos and physical states of shallow water flows, ensuring physical plausibility and temporal coherence with faster performance than traditional methods.

Contribution

It presents a novel integrated framework that incorporates physical constraints directly into the diffusion process for fluid simulation and rendering.

Findings

Outperforms data-driven baselines in realism and physical fidelity.

Produces physically plausible, temporally coherent water flow videos.

Generates videos faster than traditional simulation and rendering pipelines.

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.