GeoSinkhorn Flow: Geometry-Aware Flow Matching for Perturbation-Conditioned Dynamics in Single cell Data Phenoscapes

Single-cell technologies increasingly enable large-scale profiling of complex biological systems across many experimental perturbations, but understanding how a system reorganizes across an entire space of conditions is difficult to interpret from single-cell embeddings alone. Phenoscapes address this by embedding entire cell-state distributions, rather than individual cells, as points in a data-driven landscape. Thus, a single dot represents one experimental condition rather than one cell, yielding a map of the perturbation or patient landscape that reveals how phenotype varies continuously across conditions. Phenoscapes remain a comparatively new and underexplored representation and existing static phenoscapes position experimental conditions relative to one another without specifying trajectories that describe how a cellular population moves from one condition to another. Flow- and trajectory-based models for single-cell data are numerous, but existing approaches operate at the level of individual cells, are not built to respect the geometry of a phenoscape, and typically cannot generalize their predicted flows to conditions not seen during training. Here we introduce GeoSinkhorn Flow, a perturbation-conditioned, geometry-aware flow-matching framework specialized designed to convert a static phenoscape into a dynamic phenoscape, in which each condition-level point is additionally connected by geodesic, condition-aware transport trajectories that are consistent with the phenoscape's underlying geometry. GeoSinkhorn Flow can also model transitions directly between time points without constructing a phenoscape. GeoSinkhorn Flow uses heat-diffusion geometry to define manifold-aware transport costs and trains a geometric autoencoder whose latent Euclidean distances stay aligned with the static phenoscape geometry while extending it to unseen cells. By explicitly conditioning the learned transport dynamics on perturbation-specific gene or drug embeddings, GeoSinkhorn Flow generalizes its trajectories to new measurement conditions, produces intermediate progression states along a trajectory, and extends predictions to unseen cells and held-out perturbations. An unbalanced optimal transport variant further learns growth or transition weights, so that changes in relative cell-state abundance or transition propensity are modeled together with state movement. Across synthetic manifolds, patient-derived organoid drug responses, Perturb-seq knockdowns, and time-resolved CyTOF signaling, GeoSinkhorn Flow recovered intrinsic manifold geometry, inferred biologically coherent response trajectories, and generalized to held-out drug combinations, perturbation genes, and time points. Together, these results establish GeoSinkhorn Flow as a perturbation-conditioned, phenoscape-consistent dynamical framework, distinct from standard flow-matching approaches, for converting static phenoscapes into dynamic ones that generalize across experimental conditions.