The probability flow ODE is provably fast Sitan Chen Holden Lee Yuanzhi Li

We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling with an OU forward process. 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( d) vs. O(d), assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework.