# Physics-Informed Video Diffusion For Shallow Water Equations

arXiv: https://arxiv.org/abs/2603.15627 · HTML: https://mlsanity.com/paper/2603.15627/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [CogVideo: Large-scale Pretraining for Text-to-Video Generation via Transformers](https://mlsanity.com/paper/2205.15868/) (2022)
- [Open-Sora: Democratizing Efficient Video Production for All](https://mlsanity.com/paper/2412.20404/) (2024)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [PhysGen: Rigid-Body Physics-Grounded Image-to-Video Generation](https://mlsanity.com/paper/2409.18964/) (2024)
- [Do generative video models understand physical principles?](https://mlsanity.com/paper/2501.09038/) (2025)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [GPT4Motion: Scripting Physical Motions in Text-to-Video Generation via Blender-Oriented GPT Planning](https://mlsanity.com/paper/2311.12631/) (2023)
- [MotionCraft: Physics-based Zero-Shot Video Generation](https://mlsanity.com/paper/2405.13557/) (2024)
- [Reasoning Physical Video Generation with Diffusion Timestep Tokens via Reinforcement Learning](https://mlsanity.com/paper/2504.15932/) (2025)
- [Physics-Informed Neural Network Super Resolution for Advection-Diffusion Models](https://mlsanity.com/paper/2011.02519/) (2020)

## Built on by (most cited first, 1 of 1)

- [Self-Augmented Diffusion Guidance for Physics-Informed Generation](https://mlsanity.com/paper/2608.26748/) (2026)

## Abstract (arXiv)

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.