Convergence Analysis of Probability Flow ODE for Score-based Generative Models

arXiv:2404.09730v1 Announce Type: new
Abstract: Score-based generative models have emerged as a powerful approach for sampling high-dimensional probability distributions. Despite their effectiveness, their theoretical underpinnings remain relatively underdeveloped. In this work, we study the convergence properties of deterministic samplers based on probability flow ODEs from both theoretical and numerical perspectives. Assuming access to $L^2$-accurate estimates of the score function, we prove the total variation between the target and the generated data distributions can be bounded above by $\mathcal{O}(d\sqrt{\delta})$ in the …

abstract analysis arxiv convergence cs.lg cs.na flow generative generative models math.na numerical perspectives probability sampling study type work