Summary
Scientists often study snapshots of cells frozen at one moment in time to understand how cells change their state. But these snapshots don't tell us the exact process or path cells take to move from one state to another. The authors developed a method called Finsler Flow Matching that uses directional and randomness information from cell data to better guess the paths cells follow over time. Their approach models cell transitions more realistically by considering both the preferred directions and varying difficulties of moving between states. Tests show this method recovers intermediate cell states more accurately than previous ones, especially when changes tend to go strongly in one direction.
What this means in practice
- •For computational biologists: Generate more accurate continuous models of cell state transitions from discrete snapshot data to study developmental processes.
- •For bioinformatics software developers: Integrate directional and anisotropic dynamics into trajectory inference tools to improve prediction of cellular intermediate states.
Abstract
Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them. However, additional dynamical information can often be encoded in a cell-cell Markov transition kernel. Existing generative approaches for single cell trajectory inference either infer transport only from population marginals, impose a symmetric geometry on the state space, or incorporate directionality through a single velocity vector at each observed state. We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs. We use the first and second local moments to construct a Finsler structure motivated by the Freidlin--Wentzell action, where the second moment determines anisotropic accessibility and the first moment introduces a preferred direction of motion. We learn neural approximations of the resulting directed geodesics, use their Finsler cost to construct source-target couplings, and define geometry-aware stochastic conditional paths that can be distilled into a continuous generative process through simulation-free score and flow matching. Across synthetic and single-cell trajectory inference benchmarks, FFM improves recovery of withheld intermediate populations, particularly when the transition dynamics are strongly directional or anisotropic. Our results provide a principled route from discrete transition probabilities to continuous generative dynamics while retaining both directional and diffusive structure.