arXiv:2510. 01894v3 Announce Type: replace Abstract: Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots.
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.
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...
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.
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...
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.
arXiv:2510.01159v3 Announce Type: replace Abstract: Learning the dynamics of a process given sampled observations at several time points is an important but difficult task in many scientific applicat...
arXiv:2607. 06583v1 Announce Type: cross Abstract: DNA methylation (DNAm) serves as one of the most robust molecular biomarkers of biological aging.
arXiv:2512. 09185v4 Announce Type: replace-cross Abstract: Understanding disease progression is a central clinical challenge with direct implications for early diagnosis and personalized treatment.
arXiv:2607. 03626v1 Announce Type: new Abstract: Recent advances in generative modeling have enabled the efficient computation of Schr\"odinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching.
arXiv:2606. 15897v1 Announce Type: cross Abstract: Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance.
arXiv:2605. 00545v2 Announce Type: replace-cross Abstract: Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis.