2025/02/13 by Yuhao Liu, Liu, Yuhao, Yu Chen +5 · 2 citations
Computer Science · Decision Sciences · #Digital Filter Design and Implementation #FOS: Computer and information sciences #Machine Learning (cs.LG) #Numerical Methods and Algorithms #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2502.09130
openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions. However, prior analyses of this framework have primarily focused on the continuous-time setting, assuming a perfect solution of the underlying equations. In this work, we present the first discrete-time analysis of the stochastic interpolant framework, where we introduce an innovative discrete-time sampler and derive a finite-time upper bound on its distribution estimation error. Our result provides a novel quantification of how different factors, including the distance between source and target distributions and estimation accuracy, affect the convergence rate and also offers a new principled way to design efficient schedules for convergence acceleration. Finally, numerical experiments are conducted on the discrete-time sampler to corroborate our theoretical findings.