Schrödinger bridges on Lie group manifolds enable probabilistic intrinsic generation

chaumian · x · 2026-09-04

A new arXiv paper studies Schrödinger bridges on Lie group manifolds for probabilistic intrinsic generation. Generating directly on geometric manifolds avoids errors from flattening non-Euclidean data, repeated ambient projection, and coordinate inconsistency. The authors consider kinetic bridges with state \((gt, \xit)\), allowing endpoint observations to constrain only measured variables, with entropy projection determining conditional laws of unobserved endpoint velocities. Two computational realizations are developed: Wrapped-Kernel Bridge Calibration (WKBC) using an explicit periodized kinetic kernel on compact Abelian groups, and Reciprocal Conditional-Control Bridge Matching (RCCBM) for compact non-Abelian groups via two-sided endpoint calibration. A modular error bound in the bounded-Lipschitz path metric cleanly separates errors from endpoints, control regression, initialization, and discretization; experiments validate the approach.

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