# FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes

arXiv: https://arxiv.org/abs/2604.08586 · HTML: https://mlsanity.com/paper/2604.08586/

## Key facts

- Cited by 3 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 31 of its 46 references that are in the map.
- First posted on arXiv 30 Mar 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, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformers](https://mlsanity.com/paper/2410.10629/) (2024)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Generative AI for fast and accurate statistical computation of fluids](https://mlsanity.com/paper/2409.18359/) (2024)
- [Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2312.05320/) (2023)
- [Improving aircraft performance using machine learning: a review](https://mlsanity.com/paper/2210.11481/) (2022)
- [FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling](https://mlsanity.com/paper/2506.00862/) (2025)
- [Airfoil Diffusion: Denoising Diffusion Model For Conditional Airfoil Generation](https://mlsanity.com/paper/2408.15898/) (2024)
- [Towards certification: A complete statistical validation pipeline for supervised learning in industry](https://mlsanity.com/paper/2411.02075/) (2024)
- [Transfer learning-enhanced deep reinforcement learning for aerodynamic airfoil optimisation subject to structural constraints](https://mlsanity.com/paper/2505.02634/) (2025)
- [ONERA's CRM WBPN database for machine learning activities, related regression challenge and first results](https://mlsanity.com/paper/2505.06265/) (2025)

## Built on by (most cited first, 3 of 3)

- [Drifting Models for Surrogate Flow Modeling](https://mlsanity.com/paper/2606.07481/) (2026)
- [Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs](https://mlsanity.com/paper/2606.27126/) (2026)
- [Conditional Flow Matching for Generation of 3D Multi-variable Instantaneous Urban Microclimate Fields](https://mlsanity.com/paper/2610.10430/) (2026)

## Abstract (arXiv)

Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic surrogate models. In this work we consider a different learning paradigm and embrace generative modelling as a framework for constructing scalable fluid-dynamics surrogate models. We introduce FluidFlow, a generative model based on conditional flow-matching, a recent alternative to diffusion models that learns deterministic transport maps between noise and data distributions. FluidFlow is specifically designed to operate directly on CFD data defined on both structured and unstructured meshes alike, without the needs to perform any mesh interpolation pre-processing and preserving geometric fidelity. We assess the capabilities of FluidFlow using two different core neural network architectures, a U-Net and diffusion transformer (DiT), and condition their learning on physically meaningful parameters. The methodology is validated on two benchmark problems of increasing complexity: prediction of pressure coefficients along an airfoil boundary across different operating conditions, and prediction of pressure and friction coefficients over a full three-dimensional aircraft geometry discretized on a large unstructured mesh. In both cases, FluidFlow outperform strong multilayer perceptron baselines, achieving significantly lower error metrics and improved generalisation across operating conditions. Notably, the transformer-based architecture enables scalable learning on large unstructured datasets while maintaining high predictive accuracy. These results demonstrate that flow-matching generative models provide an effective and flexible framework for surrogate modelling in fluid dynamics, with potential for realistic engineering and scientific applications.