Multiscale Supervised Unbalanced Optimal Transport Flow Matching (MUST‑FM) is a simulation‑free framework that scales unbalanced optimal transport (UOT) for single‑cell trajectory inference by exploiting hierarchical data structure. It optionally incorporates supervised transition priors, such as cell lineages, to guide displacement fields and mass variations. Experiments demonstrate reduced computational overhead and robust, biologically meaningful trajectory inference on atlas‑scale single‑cell datasets.
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.
PACE is a trajectory inference framework that reconstructs continuous transport dynamics from destructive single‑cell time‑course snapshots. It uses a state‑ and time‑dependent anisotropic Riemannian metric to guide transport along tangent directions, alternates between refining cross‑time couplings and fitting neural bridges, and distills the learned dynamics into a global velocity field. Across multiple datasets, PACE outperforms existing methods, reducing key distance metrics by an average of 23.7% and improving RNA‑velocity alignment by 15.4%.
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.
arXiv:2602. 24201v2 Announce Type: replace Abstract: Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions.
arXiv:2607. 06583v1 Announce Type: cross Abstract: DNA methylation (DNAm) serves as one of the most robust molecular biomarkers of biological aging.
The paper introduces Distribution‑Conditioned Transport (DCT), a framework that learns transport maps conditioned on embeddings of source and target distributions, allowing generalization to unseen distribution pairs. DCT supports semi‑supervised learning for distributional forecasting by leveraging distributions observed at only one condition. It is agnostic to the transport mechanism and is demonstrated on synthetic benchmarks and four biological applications, including batch effect transfer in single‑cell genomics and modeling T‑cell receptor sequence evolution.
arXiv:2507. 04704v3 Announce Type: replace-cross Abstract: Understanding how cellular morphology, gene expression, and spatial context jointly shape tissue function is a central challenge in biology.
arXiv:2606. 05327v1 Announce Type: new Abstract: Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions.
The paper introduces Finsler Flow Matching (FFM), a method for learning continuous stochastic dynamics from discrete Markov transition graphs in single‑cell snapshot data. FFM constructs a Finsler geometry using first and second local moments, learns directed geodesics via neural networks, and employs these to build geometry‑aware stochastic paths that can be simulated without explicit score or flow matching. Benchmark tests show that FFM better recovers intermediate cellular states, especially when dynamics are directional or anisotropic.
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:2606. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.
arXiv:2506. 22228v2 Announce Type: replace-cross Abstract: Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions.