Finite-Time Convergence Analysis of ODE-based Generative Models for Stochastic Interpolants
This work addresses a theoretical gap for researchers in generative modeling, offering incremental improvements in convergence analysis for stochastic interpolants.
The paper tackled the lack of rigorous finite-time convergence guarantees for numerical implementations of ODE-based generative models using stochastic interpolants, establishing novel error bounds for forward Euler and Heun's methods and providing optimized schedules to enhance computational efficiency, with theoretical findings validated by numerical experiments.
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.