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

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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.

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Authors: Wei Huang, Andi Han, Mingyuan Bai, Huanjian Zhou, Qixin Zhang, Taiji Suzuki, Kenji Fukumizu
Released: 2026-05-22 (2mo ago)
Topic: Related to current project
Relation to my work: Read next because Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "The marker is a representational handle, not a behavioural one — sharing it between a villain persona and the assistant transfers no misalignment (HIGH confidence)", experiment "Implement Chen et al. persona-vector extraction recipe and compare to project's centroid-difference recipe". Matching terms: under, rate, project, stage, model. Source: arxiv cs.LG (Machine Learning).
arXiv: 2605.20235

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