  We provide the first polynomial-time convergence guarantees for the
probability 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.
