[2603.22962] Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data

Computer Science > Machine Learning arXiv:2603.22962 (cs) [Submitted on 24 Mar 2026] Title:Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data Authors:Anand Jerry George, Nicolas Macris View a PDF of the paper titled Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data, by Anand Jerry George and 1 other authors View PDF Abstract:We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature neural network. We derive asymptotically exact expressions for the test, train, and score errors in the high-dimensional limit. Our analysis reveals that, for linear manifolds the sample complexity required to learn the score function scales linearly with the intrinsic dimension of the manifold, rather than with the ambient dimension. Perhaps surprisingly, the benefits of low-dimensional structure starts to diminish once we have a non-linear manifold. These results indicate that diffusion models can benefit from structured data; however, the dependence on the specific type of structure is subtle and intricate. Comments: Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:2603.22962 [cs.LG]   (or arXiv:2603.22962v1 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2603.22962 Focus to learn more arXiv-is...