Schr\"odinger-Bass Bridge Barycenter Models for Measure-Valued Data

The paper introduces Schr"odinger-Bass Bridge (SBB) barycenter models—SBB-encoder, SBB-decoder, SBB-symmetric, and SBB-Markovian—for measure-valued data, leveraging directional asymmetry and dual drift-diffusion control. It proves existence of SBB-barycenters under mild assumptions, shows that for Gaussian inputs the decoder admits a Gaussian minimizer simplifying computation, and develops a hybrid Wasserstein gradient particle descent for general measures. Experiments on spatial images and single-cell RNA sequencing demonstrate that the SBB-decoder and Markovian barycenter outperform existing models in distributional interpolation and inference.

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