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  1. ; ; ; (, https://doi.org/10.48550/arXiv.2311.13745)
    Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works~\cite{chen2022,chen2022improved,benton2023linear} have studied the iteration complexity of sampling, assuming access to an accurate diffusion model. In this work, we focus on understanding the \emph{sample complexity} of training such a model; how many samples are needed to learn an accurate diffusion model using a sufficiently expressive neural network? Prior work~\cite{BMR20} showed bounds polynomial in the dimension, desired Total Variation error, and Wasserstein error. We show an \emph{exponential improvement} in the dependence on Wasserstein error and depth, along with improved dependencies on other relevant parameters. 
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    Free, publicly-accessible full text available December 9, 2025
  2. ; ; ; ; (, https://doi.org/10.48550/arXiv.2402.12727)
    Accepted Manuscript Full Text Available