The probability flow ODE is provably fast
This work addresses a theoretical bottleneck in generative modeling by proving faster convergence for ODE-based methods, which could benefit researchers and practitioners in machine learning.
The paper tackles the problem of slow convergence in probability flow ODEs for score-based generative modeling by providing the first polynomial-time convergence guarantees, achieving a better dimension dependence of O(√d) compared to prior O(d) results for DDPM.
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.