The probability flow ODE is provably fast

• URL: http://arxiv.org/abs/2305.11798v1
• Date: Fri, 19 May 2023 16:33:05 GMT
• Title: The probability flow ODE is provably fast
• Authors: Sitan Chen, Sinho Chewi, Holden Lee, Yuanzhi Li, Jianfeng Lu, Adil Salim
• Abstract summary: We provide the first-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.
• Score: 43.94655061860487
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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