LoCoFlow: Local-Context Flow Matching for Single-Cell Dynamics and Fate Inference

Single-cell sequencing profiles cellular states at discrete time points, providing population-level snapshots from which developmental and disease-associated trajectories can be reconstructed. Existing optimal-transport and flow-matching approaches typically infer temporal couplings at the level of individual cells, with limited representation of the local manifold geometry of cell-state space and the uncertainty inherent in lineage diversification. We introduce LoCoFlow, a flow-matching framework that combines local point-cloud geometry with conditional fate uncertainty. Overlapping patches define hierarchical transport between populations, and an endpoint-preserving neural bridge regularizes motion and deformation within these patches. Bridge velocities supervise a conditional field with patch-shared and cell-specific latent variables, from which alternative trajectories can be sampled without future observations. Temporal and spatial benchmarks show improvements in transport distance. On lineage-traced LARRY data, LoCoFlow reduces mean raw Brier error from 0.7990 to 0.6620 relative to scDiffEq at the same number of endpoint draws. Expression perturbations further reveal distinct roles for focal-cell and neighborhood information: geometric-patch models show aligned background and whole-patch responses, whereas random-minibatch models show opposing focal and background responses. These findings support local context as a useful representation for probabilistic fate inference and provide testable hypotheses about how it shapes predicted responses.