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DiffFluid: Plain Diffusion Models are Effective Predictors of Flow Dynamics

Dongyu Luo, Jianyu Wu, Jing Wang, Hairun Xie, Xiangyu Yue, Shixiang Tang

TL;DR

DiffFluid reframes fluid dynamics prediction as a conditional image-to-image translation task and leverages plain diffusion models with Transformers to predict flow fields from geometry and boundary/initial conditions. By training a conditional denoising diffusion model and introducing multi-resolution noise and a multi-loss strategy, DiffFluid delivers high-precision solutions for Navier–Stokes, Darcy, and Euler-based problems, achieving up to +44.8% relative improvement over prior state-of-the-art in Navier–Stokes. The approach relies on a simple, non-finetuned architecture that models the joint distribution of inputs and outputs in the data space, and it demonstrates strong generalization across resolutions and mesh types. These results suggest a scalable, high-precision solver paradigm with potential for industrial CFD acceleration and broader applications in real-time fluid dynamics prediction.

Abstract

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.

DiffFluid: Plain Diffusion Models are Effective Predictors of Flow Dynamics

TL;DR

DiffFluid reframes fluid dynamics prediction as a conditional image-to-image translation task and leverages plain diffusion models with Transformers to predict flow fields from geometry and boundary/initial conditions. By training a conditional denoising diffusion model and introducing multi-resolution noise and a multi-loss strategy, DiffFluid delivers high-precision solutions for Navier–Stokes, Darcy, and Euler-based problems, achieving up to +44.8% relative improvement over prior state-of-the-art in Navier–Stokes. The approach relies on a simple, non-finetuned architecture that models the joint distribution of inputs and outputs in the data space, and it demonstrates strong generalization across resolutions and mesh types. These results suggest a scalable, high-precision solver paradigm with potential for industrial CFD acceleration and broader applications in real-time fluid dynamics prediction.

Abstract

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.
Paper Structure (21 sections, 7 equations, 7 figures, 7 tables, 1 algorithm)

This paper contains 21 sections, 7 equations, 7 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Diffusion model
  4. Deep learning fluid dynamic solver
  5. Method
  6. Diffusion generative formulation
  7. Network architecture
  8. Detailed optimization design
  9. Experiment
  10. Fluid dynamical equation problem settings
  11. Benchmark and baselines
  12. Main results
  13. Ablation study
  14. Conclusion and future work
  15. Overview
  16. ...and 6 more sections

Figures (7)

  • Figure 1: From left to right, the $L2$ error of different models on three benchmarks: Navier-Stokes equation, Darcy flow equation and airfoil problem with Euler's equation.
  • Figure 2: Left: Structure diagram of the DiffFluid training phase. Right: Structure diagram of the DiffFluid inference phase.
  • Figure 3: A comparison of DiffFluid with the previous best model, Transolver, on the Navier-Stokes equation benchmark. Both prediction results and error maps are provided.
  • Figure 4: A comparison of the effects of different noise strategies on training loss.
  • Figure 5: Denoising performance for fluid dynamics equations: (1) Navier-Stokes Equation; (2) Darcy Flow Equation; (3) Airfoil Problem with Euler’s Equation.
  • ...and 2 more figures