用多重微分方程解外推，提升扩散模型采样精度与速度

Diffusion probabilistic models (DPMs), while effective in generating high-quality samples, often suffer from high computational costs due to their iterative sampling process. To address this, we propose an enhanced ODE-based sampling method for DPMs inspired by Richardson extrapolation, which reduces numerical error and improves convergence rates. Our method, RX-DPM, leverages multiple ODE solutions at intermediate time steps to extrapolate the denoised prediction in DPMs. This significantly enhances the accuracy of estimations for the final sample while maintaining the number of function evaluations (NFEs). Unlike standard Richardson extrapolation, which assumes uniform discretization of the time grid, we develop a more general formulation tailored to arbitrary time step scheduling, guided by local truncation error derived from a baseline sampling method. The simplicity of our approach facilitates accurate estimation of numerical solutions without significant computational overhead, and allows for seamless and convenient integration into various DPMs and solvers. Additionally, RX-DPM provides explicit error estimates, effectively demonstrating the faster convergence as the leading error term's order increases. Through a series of experiments, we show that the proposed method improves the quality of generated samples without requiring additional sampling iterations.