FlowMap: Geometry-Dynamics Consistent Embedding of RNA Velocity for Interpretable Cellular Trajectories.

Single-cell RNA sequencing reveals how cells vary across states, but these measurements capture only static snapshots of dynamic biological processes. RNA velocity addresses this limitation by estimating how gene expression is changing over time, providing directional information about cell state transitions. However, current approaches treat cellular state and dynamics separately, leading to representations that violate fundamental geometric consistency and obscure biological interpretation. Here, we present FlowMap, a framework that jointly models cellular states and their dynamics within a unified geometric representation. FlowMap simultaneously reconstructs a smooth low-dimensional manifold of gene expression and constrains RNA velocity to follow its local geometry, producing coherent and denoised representations of cellular trajectories. Across simulated and real datasets, FlowMap recovers interpretable dynamical patterns, including continuous progressions, branching events, cyclic behaviors, and stable-like states. It highlights key genes and gene programs involved in development that play distinct roles in these dynamics, and extends naturally to spatial transcriptomics, where it captures spatially organized developmental processes. Together, FlowMap establishes a principled geometric framework for modeling cellular dynamics, bridging representation learning and dynamical inference in single-cell analysis.