Schr\"odinger Bridges on Lie Group Manifolds for Probabilistic Intrinsic Generation

The paper introduces a probabilistic generative framework called Schr"odinger Bridges on Lie Group Manifolds, enabling direct modeling of non‑Euclidean data without flattening or coordinate inconsistencies. It develops two computational realizations—Wrapped‑Kernel Bridge Calibration for compact Abelian groups and Reciprocal Conditional‑Control Bridge Matching for compact non‑Abelian groups—while providing a modular error bound that separates various sources of approximation error. Experiments on protein, RNA torsions, SO(3), U(n), and protein conformational pathways demonstrate the method’s feasibility and consistency.

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