Improved Sampling of Diffusion Models in Fluid Dynamics with Tweedie's Formula

Abstract

Denoising Diffusion Probabilistic Models (DDPMs), while powerful, require extensive sampling due to a high number of function evaluations (NFEs) for accurate predictions, hindering their use in long-term spatio-temporal physics predictions. We address this limitation by introducing two novel sampling strategies: 1) Truncated Sampling Models, which achieve high-fidelity single/few-step sampling by truncating the diffusion process, bridging the gap with deterministic methods; and 2) Iterative Refinement, a reformulation of DDPM sampling as a few-step refinement process. We demonstrate that both methods significantly improve accuracy over DDPMs, DDIMs, and EDMs with NFEs $\leq$ 10 for compressible transonic flows over a cylinder and provide stable long-term predictions.