[2603.19670] Scale-Dependent Radial Geometry and Metric Mismatch in Wasserstein Propagation for Reverse Diffusion

Computer Science > Machine Learning arXiv:2603.19670 (cs) [Submitted on 20 Mar 2026] Title:Scale-Dependent Radial Geometry and Metric Mismatch in Wasserstein Propagation for Reverse Diffusion Authors:Zicheng Lyu, Zengfeng Huang View a PDF of the paper titled Scale-Dependent Radial Geometry and Metric Mismatch in Wasserstein Propagation for Reverse Diffusion, by Zicheng Lyu and Zengfeng Huang View PDF HTML (experimental) Abstract:Existing analyses of reverse diffusion often propagate sampling error in the Euclidean geometry underlying \(\Wtwo\) along the entire reverse trajectory. Under weak log-concavity, however, Gaussian smoothing can create contraction first at large separations while short separations remain non-dissipative. The first usable contraction is therefore radial rather than Euclidean, creating a metric mismatch between the geometry that contracts early and the geometry in which the terminal error is measured. We formalize this mismatch through an explicit radial lower profile for the learned reverse drift. Its far-field limit gives a contraction reserve, its near-field limit gives the Euclidean load governing direct \(\Wtwo\) propagation, and admissible switch times are characterized by positivity of the reserve on the remaining smoothing window. We exploit this structure with a one-switch routing argument. Before the switch, reflection coupling yields contraction in a concave transport metric adapted to the radial profile. At the switch, we convert once fro...