Adding one inertia step to the empirical diffusion sampler turns memorization into manifold kernel density estimation, with an O(n^{-2/(d+4)}) Wasserstein-1 rate independent of ambient dimension.
Cambridge Studies in Advanced Mathematics
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Resolving Memorization in Empirical Diffusion Model for Manifold Data in High-Dimensional Spaces
Adding one inertia step to the empirical diffusion sampler turns memorization into manifold kernel density estimation, with an O(n^{-2/(d+4)}) Wasserstein-1 rate independent of ambient dimension.