Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
📰 ArXiv cs.AI
arXiv:2605.20235v1 Announce Type: cross 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 col
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Title: Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
Abstract:
arXiv:2605.20235v1 Announce Type: cross 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 col
Abstract:
arXiv:2605.20235v1 Announce Type: cross 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 col
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