<ul><li>Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions.</li><li>This work studies DDPMs under the manifold hypothesis and proves that they achieve rates independent of the ambient dimension in terms of score learning.</li><li>In terms of sampling complexity, the rates achieved by DDPMs are independent of the ambient dimension w.r.t. the Kullback-Leibler divergence and O(sqrt(D)) w.r.t. the Wasserstein distance.</li><li>A new framework connecting diffusion models to the theory of extrema of Gaussian Processes is developed.</li></ul>

Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions

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