Convergence Analysis for Fast High-Order ODE Solvers in Diffusion Probabilistic Models

This talk presents a rigorous convergence analysis for fast, high-order ODE solvers in diffusion probabilistic models. It quantifies the interplay between the L2 score matching error (from neural network training) and the discretization error of Runge-Kutta integrators, establishing total variation distance bounds that only require C^2 regularity for the learned score functions. Numerical experiments validate the theoretical rates and the C^2 assumption on benchmark datasets. This work provides a solid theoretical foundation for designing efficient and accurate deterministic diffusion samplers.