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%.
By Chenglei Yu, Chuanrui Wang, Bangyan Liao, Tailin Wu
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.
By Niklas Canova, Jonas Simon Fleck
The paper introduces Kinematic Interpolants (KI), a new framework that extends stochastic interpolants to infer nonlinear dynamics from multiple snapshots in phase space, incorporating both position and velocity measurements. KI addresses the ambiguity in dynamics inference from real-world data and is scalable without simulation or unnecessary approximations. Experiments on various scientific datasets show that KI reconstructs underlying dynamics more accurately than existing baselines while requiring significantly less training time.
By Yiheng (Roger), Jiang, Youssef Marzouk, Avishek Joey Bose, Aram-Alexandre Pooladian
arXiv:2610.19878v1 Announce Type: new
Abstract: Population dynamics are often observed only as unpaired snapshots, which leave the evolution between measurements underdetermined. Second-order regular...
By Amartya Banerjee, Harlin Lee, Caroline Moosm\"uller
The paper introduces scEGFlow, an energy‑guided flow matching framework that predicts how single cells respond to perturbations by modeling continuous transitions from control to perturbed states. It uses conditional flow matching and condition‑specific energy gradients to dynamically adjust predictions without retraining, achieving superior performance on imaging and transcriptomic benchmarks, even for unseen perturbations or limited data. The method preserves cellular manifold geometry, heterogeneity, and accurately recapitulates gene‑expression regulatory patterns.
By Jianan Wei, Jiajun Hong, Guikun Chen, Ning Yang, Lifeng Fan, Wenguan Wang
arXiv:2602.08318v3 Announce Type: replace-cross
Abstract: Flow matching (FM) is increasingly used in scientific domains for time series generation and forecasting, where data often arise from underly...
By Soon Hoe Lim, Shizheng Lin, Michael W. Mahoney, N. Benjamin Erichson
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...
By Oskar Kviman, Kirill Tamogashev, Nicola Branchini, V\'ictor Elvira, Jens Lagergren, Esmeralda S. Whitammer
arXiv:2607. 26398v1 Announce Type: new Abstract: Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration.
By Mark Goldstein, Anshuk Uppal, Raghav Singhal, Aahlad Puli, Rajesh Ranganath
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.
By Qiangwei Peng, Lezhi Chen, Peijie Zhou
arXiv:2610.00785v1 Announce Type: new
Abstract: Flow matching (FM) learns generative transport by fitting continuous-time motion from a simple source distribution to the data distribution. Most exist...
By Haoyang Jiang, Yuheng Li, Di Yang, Yanhai Xiong, Haipeng Chen, Yi He
arXiv:2611.05439v1 Announce Type: new
Abstract: High-fidelity simulation of dynamical systems is central to scientific discovery and engineering design, yet remains computationally demanding. Here we...
By Chawit Kaewnuratchadasorn, Jiaji Wang, Xin Nie
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