Finite-Time Convergence Analysis of ODE-based Generative Models for Stochastic Interpolants

Yuhao Liu, Yu Chen, Rui Hu, Longbo Huang

Keywords: Stochastic Interpolants, Diffusion Models, Deterministic Sampler

Abstract: Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions via ordinary or stochastic differential equations (ODEs/SDEs), holding significant promise for generative modeling. While previous studies have analyzed the finite-time convergence rate of discrete-time implementations for SDEs, the ODE counterpart remains largely unexplored. In this work, we bridge this gap by presenting a rigorous finite-time convergence analysis of numerical implementations for ODEs in the framework of stochastic interpolants. We establish novel discrete-time total variation error bounds for two widely used numerical solvers: the first-order forward Euler method and the second-order Heun's method. Our analysis also yields optimized iteration complexity results and step size schedules that enhance computational efficiency. Notably, when specialized to the diffusion model setting, our theoretical guarantees for the second-order method improve upon prior results in terms of both smoothness requirements and dimensional dependence. Our theoretical findings are corroborated by numerical and image generation experiments, which validate the derived error bounds and complexity analyses.

Primary Area: generative models

Submission Number: 10901