Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity

ArXi:2603.20645v1 Announce Type: new Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates how diffusion models learn such structured data, focusing on two key aspects: statistical complexity and influence of data geometric properties.