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

ArXi:2603.19670v1 Announce Type: new 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.