Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions

TL;DR

This work tackles the computational bottleneck of diffusion probabilistic models by introducing RX-DPM, an extrapolation-based sampling method inspired by Richardson extrapolation. RX-DPM leverages multiple intermediate ODE solutions at the same denoising time to extrapolate towards a more accurate prediction, and it generalizes to non-uniform time grids and arbitrary solvers without increasing NFEs. The authors provide a theoretical analysis of truncation errors on non-uniform grids and demonstrate that RX-Euler achieves higher-order convergence, with extensions to Runge-Kutta and Adams-Bashforth-based solvers. Extensive experiments across EDM, Stable Diffusion, DPM-Solvers, and PNDM show consistent improvements in sample quality at low NFEs and only minor computational overhead, including a hybrid RX+EDM strategy that yields further gains. Overall, RX-DPM offers a practical, solver-agnostic approach to faster yet more accurate diffusion sampling with explicit error estimates.

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.

Figures (14)

• Figure 1: Application of the proposed extrapolation on two denoising steps ($k=2$) with time steps of $[t_{i},t_{i-1},t_{i-2}]$. $\hat{\bm{x}}_{t_{i-2}}^{(n)}$ denotes that $n$ steps are used by the baseline sampler within the same interval. $\tilde{\bm{x}}_{t_{i-2}}^{(2)}$ represents the extrapolated estimation using two ODE solutions at $t_{i-2}$, $\hat{\bm{x}}_{t_{i-2}}^{(1)}$ and $\hat{\bm{x}}_{t_{i-2}}^{(2)}$.
• Figure 2: Effect of extrapolation on the Euler method with different $k$'s.
• Figure 3: FIDs of RX-Euler, Heun's method (labeled as EDM), LA-DPM and IIA (or BIIA) by varying NFEs on the CIFAR-10, FFHQ, AFHQv2, and ImageNet datasets using the EDM backbone.
• Figure 4: Qualitative results of DDIM and RX-DDIM based on Stable Diffusion V2. RX-DDIM produces sharper and more detailed backgrounds, especially evident in the left example. On the right, RX-DDIM generates more realistic giraffes, whereas DDIM struggles at $\text{NFEs}=50$, failing to properly render the giraffe.
• Figure 5: Digarams of the baseline and the proposed sampling methods. The blue-bordered boxes in (b) and (c) indicate that the corresponding operation does not require network evaluation. The ODE solver in (c) refers to the deterministic sampling component of the SDE solver.