# Predicting Flow Dynamics using Diffusion Models

arXiv: https://arxiv.org/abs/2507.08106 · HTML: https://mlsanity.com/paper/2507.08106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 2 of its 2 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## 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, 2 of 2)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DiffFluid: Plain Diffusion Models are Effective Predictors of Flow Dynamics](https://mlsanity.com/paper/2409.13665/) (2024)

## Abstract (arXiv)

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising diffusion probabilistic model (DDPM) framework to tackle Navier-Stokes and Darcy flow equations. Our goal was to validate the reproducibility of the methods in the DiffFluid paper while testing its viability for other simulation types, particularly the Lattice Boltzmann method. Despite our computational limitations and time constraints, this work provides evidence of the flexibility and potential of the model as a general-purpose solver for fluid dynamics. Our results show both the potential and challenges of applying diffusion models to complex fluid dynamics problems. This work highlights the opportunities for future research in optimizing the computational efficiency and scaling such models in broader domains.