When Scores Learn Geometry: Rate Separations under the Manifold Hypothesis

ArXi:2509.24912v2 Announce Type: replace-cross Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success arises from implicitly learning the data manifold rather than the full distribution.