The probability flow ODE is provably fast

Sitan Chen, Sinho Chewi, Holden Lee, Yuanzhi Li, Jianfeng Lu, Adil Salim

Keywords: DDIM, deterministic samplers, diffusion models, predictor-corrector, probability flow ODE, score-based generative modeling

TL;DR: We give the first fully polynomial-time bounds for the probability flow ODE, together with a corrector based on underdamped Langevin, and obtain superior dimension dependence compared to existing analyses of SDE-based diffusion models.

Abstract: We provide the first polynomial-time convergence guarantees for the probabilistic flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining such guarantees for the SDE-based implementation (i.e., denoising diffusion probabilistic modeling or DDPM), but requires the development of novel techniques for studying deterministic dynamics without contractivity. Through the use of a specially chosen corrector step based on the underdamped Langevin diffusion, we obtain better dimension dependence than prior works on DDPM ($O(\sqrt d)$ vs. $O(d)$, assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework.

Submission Number: 5773