# A Denoising Diffusion Model for Fluid Field Prediction

arXiv: https://arxiv.org/abs/2301.11661 · HTML: https://mlsanity.com/paper/2301.11661/

## Key facts

- Cited by 32 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 27 of its 42 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## 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, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Score-based Generative Neural Networks for Large-Scale Optimal Transport](https://mlsanity.com/paper/2110.03237/) (2021)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow](https://mlsanity.com/paper/1801.09710/) (2018)
- [Deep Learning the Physics of Transport Phenomena](https://mlsanity.com/paper/1709.02432/) (2017)
- [Generative Modeling of Turbulence](https://mlsanity.com/paper/2112.02548/) (2021)
- [Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network](https://mlsanity.com/paper/2004.00707/) (2020)
- [DualSmoke: Sketch-Based Smoke Illustration Design with Two-Stage Generative Model](https://mlsanity.com/paper/2208.10906/) (2022)
- [Parameter-Conditioned Sequential Generative Modeling of Fluid Flows](https://mlsanity.com/paper/1912.06752/) (2019)

## Built on by (most cited first, 30 of 32)

- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems](https://mlsanity.com/paper/2312.10527/) (2023)
- [Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints](https://mlsanity.com/paper/2506.04171/) (2025)
- [From Zero to Turbulence: Generative Modeling for 3D Flow Simulation](https://mlsanity.com/paper/2306.01776/) (2023)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Text2PDE: Latent Diffusion Models for Accessible Physics Simulation](https://mlsanity.com/paper/2410.01153/) (2024)
- [Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator](https://mlsanity.com/paper/2408.02965/) (2024)
- [A Probabilistic Approach to Wildfire Spread Prediction Using a Denoising Diffusion Surrogate Model](https://mlsanity.com/paper/2507.00761/) (2025)
- [Guiding diffusion models to reconstruct flow fields from sparse data](https://mlsanity.com/paper/2510.19971/) (2025)
- [Turbulence Scaling from Deep Learning Diffusion Generative Models](https://mlsanity.com/paper/2311.06112/) (2023)
- [Generating Physical Dynamics under Priors](https://mlsanity.com/paper/2409.00730/) (2024)
- [Diffusion model based data generation for partial differential equations](https://mlsanity.com/paper/2306.11075/) (2023)
- [Particle-Guided Diffusion Models for Partial Differential Equations](https://mlsanity.com/paper/2601.23262/) (2026)
- [Physics-informed diffusion models in spectral space](https://mlsanity.com/paper/2602.09708/) (2026)
- [Hyena Neural Operator for Partial Differential Equations](https://mlsanity.com/paper/2306.16524/) (2023)
- [Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systems](https://mlsanity.com/paper/2405.07097/) (2024)
- [Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates](https://mlsanity.com/paper/2405.17260/) (2024)
- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [The Universal Statistical Structure and Scaling Laws of Chaos and Turbulence](https://mlsanity.com/paper/2311.01358/) (2023)
- [Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction](https://mlsanity.com/paper/2505.24145/) (2025)
- [PIRF: Physics-Informed Reward Fine-Tuning for Diffusion Models](https://mlsanity.com/paper/2509.20570/) (2025)
- [Reframing Generative Models for Physical Systems using Stochastic Interpolants](https://mlsanity.com/paper/2509.26282/) (2025)
- [Generative Urban Flow Modeling: From Geometry to Airflow with Graph Diffusion](https://mlsanity.com/paper/2512.14725/) (2025)
- [Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems](https://mlsanity.com/paper/2511.04641/) (2025)
- [Efficient Probabilistic Modeling of Crystallization at Mesoscopic Scale](https://mlsanity.com/paper/2405.16608/) (2024)
- [FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fields](https://mlsanity.com/paper/2510.04325/) (2025)
- [Coupled Diffusion-Encoder Models for Reconstruction of Flow Fields](https://mlsanity.com/paper/2601.07946/) (2026)
- [UniFluids: Unified Neural Operator Learning with Conditional Flow-matching](https://mlsanity.com/paper/2603.22309/) (2026)

## Abstract (arXiv)

We propose a novel denoising diffusion generative model for predicting nonlinear fluid fields named FluidDiff. By performing a diffusion process, the model is able to learn a complex representation of the high-dimensional dynamic system, and then Langevin sampling is used to generate predictions for the flow state under specified initial conditions. The model is trained with finite, discrete fluid simulation data. We demonstrate that our model has the capacity to model the distribution of simulated training data and that it gives accurate predictions on the test data. Without encoded prior knowledge of the underlying physical system, it shares competitive performance with other deep learning models for fluid prediction, which is promising for investigation on new computational fluid dynamics methods.