# Schrödinger Bridge

On 5,357 structurally resolved small molecules from DrugBank 5.1.10, Schrödinger Bridge Onsager Flow drives the transport from a uniform chemical library toward a drug-likeness distribution to a total variation distance of 0.0141, against 0.1753 for a Sinkhorn baseline at its best setting across a ten-value regularization sweep. The method keeps one scalar potential per molecule updated by mirror descent instead of an all-pairs coupling matrix; its neural amortization, SBOFNet, returns a total variation distance of 0.0380 in a single forward pass with 1.6M parameters, at lower accuracy than the analytic solver.

On 5,357 structurally resolved small molecules from DrugBank 5.1.10, Schrödinger Bridge Onsager Flow drives the transport from a uniform chemical library toward a drug-likeness distribution to a total variation distance of 0.0141, against 0.1753 for a Sinkhorn baseline at its best setting across a ten-value regularization sweep. The method keeps one scalar potential per molecule updated by mirror descent instead of an all-pairs coupling matrix; its neural amortization, SBOFNet, returns a total variation distance of 0.0380 in a single forward pass with 1.6M parameters, at lower accuracy than the analytic solver.

The work proposes KANResDiff, which learns local residual diffusion via Kolmogorov-Arnold Networks for ambiguous medical image segmentation: it replaces MLP linear time embeddings with B-spline-based Independent Time Encoding to strengthen independence across inference stages, and injects a deterministic residual prior with learnable weights through a Residual Schrödinger Bridge, achieving state-of-the-art GED and HM-IoU on the two public datasets LIDC and ISIC3 with maximum improvements of 16.8% and 7.7% respectively while keeping competitive MDM performance.

The work proposes KANResDiff, which learns local residual diffusion via Kolmogorov-Arnold Networks for ambiguous medical image segmentation: it replaces MLP linear time embeddings with B-spline-based Independent Time Encoding to strengthen independence across inference stages, and injects a deterministic residual prior with learnable weights through a Residual Schrödinger Bridge, achieving state-of-the-art GED and HM-IoU on the two public datasets LIDC and ISIC3 with maximum improvements of 16.8% and 7.7% respectively while keeping competitive MDM performance.