2025/08/10 by Yuhao Liu, Liu, Yuhao, Hu, Rui +4
Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical methods for differential equations #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2508.07333
openalex publication_date 2025/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence guarantees for practical numerical schemes remain largely unexplored. In this work, we address the finite-time convergence analysis of numerical implementations for ordinary differential equations (ODEs) derived from stochastic interpolants. Specifically, we establish novel finite-time error bounds in total variation distance for two widely used numerical integrators: the first-order forward Euler method and the second-order Heun's method. Furthermore, our analysis on the iteration complexity of specific stochastic interpolant constructions provides optimized schedules to enhance computational efficiency. Our theoretical findings are corroborated by numerical experiments, which validate the derived error bounds and complexity analyses.