Single-cell snapshot data can reveal a continuum of cellular states, but they do not uniquely determine the dynamics that move cells between those states. This makes trajectory inference from a single time point inherently underdetermined.
The paper proposes Finsler Flow Matching, a method that performs dynamics-aware geodesic interpolation for single-snapshot trajectory inference. By using Finsler geometry, the interpolation is designed to respect the underlying dynamics rather than treating the state space as flat.
The authors note that additional dynamical information can often be encoded in cell-cell data, and their approach aims to exploit that information to narrow down the possible transition paths.