Faster Diffusion Models via Higher-Order Approximation

• URL: http://arxiv.org/abs/2506.24042v1
• Date: Mon, 30 Jun 2025 16:49:03 GMT
• Title: Faster Diffusion Models via Higher-Order Approximation
• Authors: Gen Li, Yuchen Zhou, Yuting Wei, Yuxin Chen,
• Abstract summary: We propose a principled, training-free sampling algorithm that requires only the order of d1+2/K varepsilon-1/K $$ score function evaluations.<n>Our theory is robust vis-a-vis inexact score estimation, degrading gracefully as the score estimation error increases.
• Score: 28.824924809206255
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we propose a principled, training-free sampling algorithm that requires only the order of $$ d^{1+2/K} \varepsilon^{-1/K} $$ score function evaluations (up to log factor) in the presence of accurate scores, where $K$ is an arbitrarily large fixed integer. This result applies to a broad class of target data distributions, without the need for assumptions such as smoothness or log-concavity. Our theory is robust vis-a-vis inexact score estimation, degrading gracefully as the score estimation error increases -- without demanding higher-order smoothness on the score estimates as assumed in previous work. The proposed algorithm draws insight from high-order ODE solvers, leveraging high-order Lagrange interpolation and successive refinement to approximate the integral derived from the probability flow ODE.

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