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: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.
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional.
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.
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%.
arXiv:2608. 15306v1 Announce Type: cross Abstract: High-throughput single-cell and spatial transcriptomic technologies provide high-resolution snapshots of heterogeneous cellular states, but their destructive nature prevents repeated measurements of the same cells over time.
The paper introduces Double‑Stitch, a simulation‑free method for learning population dynamics in Wasserstein space. It penalizes the residual of the equation of motion along a learned path, derived from a Clebsch variational principle that avoids gradient velocities. Experiments on synthetic, single‑cell, and ocean vortex data show that Double‑Stitch matches or surpasses gradient‑flow and simulation‑based methods while training 4–14 times faster.
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.
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:2607. 06583v1 Announce Type: cross Abstract: DNA methylation (DNAm) serves as one of the most robust molecular biomarkers of biological aging.
The paper presents Variational Doob-Wasserstein Flow (VDWF), a simulation-free method for learning unbalanced population dynamics on the Riemannian Wasserstein-Fisher-Rao manifold. VDWF first learns a geometry model with a data-dependent metric to capture intrinsic dynamics, then uses Doob's h-transform to incorporate boundary information for trajectory inference. It employs a growth model to learn dynamics and construct intermediate mass samples in WFR space, analyzes convergence via a uniform Log-Sobolev inequality, and demonstrates competitive performance on real-world datasets for both balanced and unbalanced dynamics.
arXiv:2608.21070v1 Announce Type: cross Abstract: Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics. While Optimal T...