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 TP‑DATE, a dynamic framework that extends Gromov–Wasserstein optimal transport (GW‑OT) to reconstruct continuous trajectories without simulation. It formulates a broad class of static and dynamic Quadratic‑form OT (QOT) via path actions, proving static‑dynamic equivalence, and develops travelling‑pair flow matching to capture interacting conditional paths in a single vector field. Experiments on synthetic and real spatial transcriptomics data show that TP‑DATE better preserves spatial structure and improves 3D dynamics reconstruction.
By Junda Ying, Zhiwei Zeng, Peijie Zhou, Lei Zhang
Dynamic Generalized Gromov-Wasserstein Optimal Transport extends classical optimal transport by incorporating structure-aware transport costs, which is especially relevant for spatial transcriptomics where preserving tissue structure is crucial. The paper introduces TP-DATE, a simulation-free framework that generalizes GW-OT dynamically, formulating static and dynamic Quadratic-form OT through path actions and proving their equivalence. TP-DATE employs travelling-pair flow matching to enable interacting conditional paths, resulting in better preservation of spatial structure and improved continuous 3D dynamics reconstruction on both synthetic and real spatial transcriptomics data.
arXiv:2602.15396v2 Announce Type: replace
Abstract: Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces in...
By Jeongwoo Shin, Jinhwan Sul, Joonseok Lee, Jaewong Choi, Jaemoo Choi
arXiv:2606. 11286v1 Announce Type: cross Abstract: High-content imaging assays quantify cellular responses to chemical and genetic perturbations, yet continuous trajectories of individual cells are unobservable because cells are chemically fixed at acquisition.
By Xurui Wang, Qin Ren, Jun Ma, Haibin Ling, Chenyu You