Euclidean Drifting Is a Strong Topological Baseline

Recent topological extensions of flow matching and Schrödinger bridge matching report gains on graph- and cochain-structured data. We test whether analogous changes help Drifting Models, which generate a sample with one network evaluation. We modify the loss with a Hodge–Sobolev metric and heat kernel, and modify the predictor with graph propagation. With affinities fixed, the Hodge loss rescales each spectral component of the Euclidean output direction by a positive factor. In seven matched comparisons across five benchmarks, every confidence interval for the Hodge–Euclidean difference contains zero; four also lie within a ±1% margin. On earthquakes, graph propagation improves the predictor, but the native-versus-permuted confidence interval contains zero. On brain data, Euclidean-loss Drifting attains a lower debiased Sinkhorn-1 estimate than our I-TFM reproduction.