Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access

TL;DR

This paper offers a new theoretical analysis of diffusion models, establishing a sample complexity bound of O(ε^{-4}) without requiring access to empirical risk minimizers, improving understanding of their training efficiency.

Contribution

It provides the first sample complexity bound for diffusion model training that does not assume access to the empirical risk minimizer, using a structured error decomposition.

Findings

Achieves a sample complexity of O(ε^{-4}) for score estimation.

Eliminates exponential dependence on neural network parameters in analysis.

First result to remove the need for empirical risk minimizer access in this context.

Abstract

Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data dimension or rely on unrealistic assumptions such as access to exact empirical risk minimizers. In this work, we provide a principled analysis of score estimation, establishing a sample complexity bound of $\mathcal{O}(\epsilon^{-4})$. Our approach leverages a structured decomposition of the score estimation error into statistical, approximation, and optimization errors, enabling us to eliminate the exponential dependence on neural network parameters that arises in prior analyses. It is the first such result that achieves sample complexity bounds without assuming access to the empirical risk minimizer of score function estimation loss.