The probability flow ODE is provably fast

05/19/2023

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by   Sitan Chen, et al.

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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(√(d)) vs. O(d), assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework.