Score Approximation for Diffusion Models on Arbitrary Low-Dimensional Structures

arXiv:2606.19894 · cs.LG · Submitted 2026-06-18 · Read on arXiv

cs.LG

Submitted: 2026-06-18

Updated: 2026-10-05

Terminology

• Diffusion Model — 3× in this paper · explained in 9 episodes
• Diffusion Models — 3× in this paper · explained in 6 episodes
• Score Function — 1× in this paper · explained in 4 episodes

Sources

• Graph Laplacians on Singular Manifolds: Toward understanding complex spaces: graph Laplacians on manifolds with singularities and boundaries
• Transformers are Inherently Succinct
• Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
• Back to Basics: Let Denoising Generative Models Denoise
• Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity

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