DiffFluid: Plain Diffusion Models are Effective Predictors of Flow Dynamics

TL;DR

DiffFluid demonstrates that plain diffusion models with Transformers can effectively predict complex fluid flow dynamics across various conditions, offering a simpler yet highly accurate alternative to traditional solvers.

Contribution

This work introduces a novel approach using plain diffusion models for fluid dynamics prediction, simplifying model design while maintaining high accuracy and outperforming existing methods.

Findings

Achieves +44.8% relative accuracy in Navier-Stokes equations

Improves +14.0% in Darcy flow predictions

Enhances +11.3% in airfoil problem with Euler's equation

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.