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.
LapDDPM is a conditional Graph Diffusion Probabilistic Model that generates high‑fidelity, biologically plausible single‑cell RNA sequencing data. It incorporates graph‑based inductive biases and a spectral adversarial perturbation mechanism to enforce robustness against structural noise, effectively acting as a Distributionally Robust Optimization framework. The model extends to spatial transcriptomics and multi‑modal data, and experimental results on datasets such as PBMC3K, Dentate Gyrus, HLCA, Visium, and 10x Multiome show it outperforms state‑of‑the‑art baselines in distribution matching, manifold preservation, and downstream utility.
By Lorenzo Bini, Stephane Marchand-Maillet
arXiv:2506. 11152v4 Announce Type: replace-cross Abstract: Single-cell transcriptomics and proteomics have become a great source for data-driven insights into biology, enabling the use of advanced deep learning methods to understand cellular heterogeneity and gene expression at the single-cell level.
By Hiren Madhu, Jo\~ao Felipe Rocha, Tinglin Huang, Siddharth Viswanath, Smita Krishnaswamy, Rex Ying
The paper introduces SUDO, a simulation‑free framework for unbalanced dynamic optimal transport (UDOT) that supports general convex growth penalties beyond the quadratic Wasserstein‑Fisher‑Rao case. By showing that concave penalties lead to degenerate solutions, the authors focus on convex penalties, learning conditional paths and transport costs to solve a semi‑coupling problem and then applying unbalanced flow matching. On benchmark datasets, SUDO matches the accuracy of analytical WFR solvers while being faster than simulation‑based methods, and it also handles asymmetric penalties that better reflect proliferation‑dominant biological priors.
By Junda Ying, Yuxuan Wang, Bowen Yang, Peijie Zhou, Lei Zhang
arXiv:2607. 06583v1 Announce Type: cross Abstract: DNA methylation (DNAm) serves as one of the most robust molecular biomarkers of biological aging.
By Chandan Gupta, Syed Haider, Pietro Li\`o