Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access
This work addresses a key theoretical bottleneck for researchers and practitioners in machine learning by improving the sample efficiency of diffusion models, which are widely used in vision, language, and scientific applications, though it is incremental as it builds on prior analyses.
The paper tackles the problem of high sample complexity in diffusion model training by providing a theoretical analysis that eliminates unrealistic assumptions like access to exact empirical risk minimizers, achieving a sample complexity bound of O(ε⁻⁴) and removing exponential dependence on neural network parameters.
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 $\mathcal{O}(ε^{-4})$. 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.