The probability flow ODE is provably fast

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper Supplemental


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


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.