Finsler Flow Matching: Dynamics-Aware Geodesic Interpolation for Single-Snapshot Trajectory Inference

Key points

• Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them.1
• 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.1
• 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.1
• 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.1

Sources (1)

• [1]Finsler Flow Matching: Dynamics-Aware Geodesic Interpolation for Single-Snapshot Trajectory Inference
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 06:23 AM

  We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs.

  Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them.

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