{"id":974445,"date":"2023-10-09T15:22:54","date_gmt":"2023-10-09T22:22:54","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=974445"},"modified":"2024-01-22T12:05:48","modified_gmt":"2024-01-22T20:05:48","slug":"the-probability-flow-ode-is-provably-fast","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/the-probability-flow-ode-is-provably-fast\/","title":{"rendered":"The probability flow ODE is provably fast"},"content":{"rendered":"

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<\/span>(<\/span>d<\/span><\/span>\u2212\u2212\u221a<\/span>)<\/span><\/span><\/span><\/span>\u00a0vs.\u00a0O<\/span>(<\/span>d<\/span>)<\/span><\/span><\/span><\/span>, assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework.<\/p>\n","protected":false},"excerpt":{"rendered":"

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 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