Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions

2025-04-02

AI Summary

Diffusion model sampling suffers from high computational cost and slow convergence due to iterative ODE solving. This paper proposes RX-DPM, a Richardson extrapolation–enhanced sampling method based on multistep ODE numerical integration. It is the first to adapt generalized Richardson extrapolation to diffusion ODE solvers under arbitrary time-step schedulers; introduces a local truncation error–driven adaptive extrapolation framework that provides explicit error estimation and provably higher-order convergence; and achieves all this without increasing the number of function evaluations (NFE). On multiple benchmarks, RX-DPM significantly outperforms mainstream solvers—including DDIM and DPM-Solver++—at identical NFE, yielding lower FID and LPIPS scores and improved sample quality. The core contribution lies in systematically integrating classical numerical analysis techniques into diffusion sampling, enabling high-accuracy, high-order-convergent, and zero-overhead acceleration.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Reduce computational costs in diffusion probabilistic models sampling
• Improve sample quality without increasing function evaluations
• Generalize Richardson extrapolation for arbitrary time step scheduling

Innovation

• Enhanced ODE-based sampling with Richardson extrapolation
• Leverages multiple ODE solutions for denoised prediction
• General formulation for arbitrary time step scheduling