Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
A new paper presents a framework called Score-induced Latent Diffusion (SiLD) for learning diffusion models under the manifold hypothesis. This framework addresses the challenge of efficiently learning the score function in high-dimensional data supported on low-dimensional manifolds. Experimental results demonstrate that SiLD matches or outperforms existing models in terms of generation quality and reconstruction accuracy.
- ▪The paper introduces a collapse-and-refine mechanism that leverages the geometry of the score function.
- ▪SiLD replaces the heuristic KL regularization used in VAE-based latent diffusion models with a single denoising score matching objective.
- ▪The sample complexity of the proposed method depends on the intrinsic dimension rather than the ambient dimension.
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Computer Science > Machine Learning arXiv:2605.20235 (cs) [Submitted on 16 May 2026] Title:Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine Authors:Wei Huang, Andi Han, Mingyuan Bai, Huanjian Zhou, Qixin Zhang, Taiji Suzuki, Kenji Fukumizu View a PDF of the paper titled Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine, by Wei Huang and 6 other authors View PDF HTML (experimental) 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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