Physics-Informed Video Diffusion For Shallow Water Equations

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.

Figures (2)

• Figure 1: Model architecture. We condition the DiT on the initial and boundary conditions ($Q^0$ and $D_b$) of the SWEs, and a rendered frame $I^0$, to jointly generate the video $V$ and physical states $P$.
• Figure 2: Qualitative comparison of Gaussian bumps results.