Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine

arXiv:2605.20235v1 Announce Type: new Abstract: Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains theoretically unexplained. We identify a collapse-and-refine mechanism driven by the geometry of the score function itself: at small noise scales, the diverging singularity of the score drives a rapid dimensional collapse of the induced denoising map onto the data manifold projection; at moderate noise scales, traini

Source: arXiv cs.LG — read the full report at the original publisher.

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