arXiv:2605. 02961v2 Announce Type: replace-cross Abstract: Most modern bridge-diffusion methods achieve finite-time transport by specifying an interpolation, Schrodinger-bridge, or stochastic-control objective and then learning the associated score or drift field with a neural network.
By Michael Chertkov
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.
By Shizhe Zhang, Mingyang Zhao, Lei Ma
arXiv:2607. 16987v1 Announce Type: cross Abstract: Over the past few years, diffusion-based Schr\"odinger bridge models have been proposed to approximate optimal transport dynamics between two prescribed boundary distributions, with successful applications to generative modeling.
By Maxence Noble, Marie Scheid, Yazid Janati, Eric Moulines, Alain Durmus
arXiv:2509.26364v3 Announce Type: replace
Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...
By Kirill Tamogashev, Esmeralda S. Whitammer
The paper introduces the Distributionally Robust Schr"odinger Bridge (DRSB), a method that learns a single controller capable of handling uncertainty in the initial distribution for stochastic transport tasks. DRSB’s objective combines control energy with a KL penalty on the terminal distribution, and it seeks to minimize the worst‑case value of this objective over an ambiguity set around the nominal initial distribution. The authors derive a variational formulation, connect it to stochastic optimal control and distributionally robust optimization, and propose an alternating algorithm with Wasserstein and Sinkhorn variants. Experiments on two‑dimensional transport and image‑to‑image translation demonstrate improved robustness to input perturbations compared to standard SB, while also achieving lower mean sliced Wasserstein distance on Gaussian mixture transport.
By Jinhwan Sul, Panagiotis Theodoropoulos, Vincent Pacelli, Jaemoo Choi, Evangelos Theodorou
arXiv:2609.13758v1 Announce Type: cross
Abstract: We establish the equivalence between the stochastic optimal control and path space formulations of the Schr\"odinger bridge problem (SBP) for the kin...
By Hamza Mahmood, Georgiy A. Bondar, Abhishek Halder, Adeel Akhtar