The probability flow ODE is provably fast

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

Authors

• Sitan Chen
• Sinho Chewi
• Holden Lee
• Yuanzhi Li Carnegie Mellon University, Pittsburgh, PA, USA
• Jianfeng Lu Wuhan University of Science and Technology Key Laboratory of Social Computing and Cognitive Intelligence (Dalian University of Technology), Ministry of Education, China
• Adil Salim

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