# DiffFluid: Plain Diffusion Models are Effective Predictors of Flow Dynamics

arXiv: https://arxiv.org/abs/2409.13665 · HTML: https://mlsanity.com/paper/2409.13665/

## Key facts

- Cited by 4 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 37 of its 51 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## 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, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generators](https://mlsanity.com/paper/2303.13439/) (2023)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Effective Data Augmentation With Diffusion Models](https://mlsanity.com/paper/2302.07944/) (2023)
- [DiffIR: Efficient Diffusion Model for Image Restoration](https://mlsanity.com/paper/2303.09472/) (2023)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)

## Built on by (most cited first, 4 of 4)

- [FLEX: A Backbone for Diffusion-Based Modeling of Spatio-temporal Physical Systems](https://mlsanity.com/paper/2505.17351/) (2025)
- [Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems](https://mlsanity.com/paper/2511.04641/) (2025)
- [HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization](https://mlsanity.com/paper/2607.07233/) (2026)
- [Predicting Flow Dynamics using Diffusion Models](https://mlsanity.com/paper/2507.08106/) (2025)

## Abstract (arXiv)

We showcase the plain diffusion models with Transformers are effective predictors of fluid dynamics under various working conditions, e.g., Darcy flow and high Reynolds number. Unlike traditional fluid dynamical solvers that depend on complex architectures to extract intricate correlations and learn underlying physical states, our approach formulates the prediction of flow dynamics as the image translation problem and accordingly leverage the plain diffusion model to tackle the problem. This reduction in model design complexity does not compromise its ability to capture complex physical states and geometric features of fluid dynamical equations, leading to high-precision solutions. In preliminary tests on various fluid-related benchmarks, our DiffFluid achieves consistent state-of-the-art performance, particularly in solving the Navier-Stokes equations in fluid dynamics, with a relative precision improvement of +44.8%. In addition, we achieved relative improvements of +14.0% and +11.3% in the Darcy flow equation and the airfoil problem with Euler's equation, respectively. Code will be released at https://github.com/DongyuLUO/DiffFluid upon acceptance.