Inferring cell trajectories from snapshots using geometry-aware transport

Single-cell trajectory inference reconstructs developmental paths from time-course snapshots without observing individual cells across time. PACE addresses misalignment caused by asynchronous development by learning a state- and time-dependent Riemannian metric that favors transport along local developmental directions. The method alternates between refining cell correspondences across timepoints and fitting neural bridges between adjacent snapshots, then distills the result into a global velocity field. Tested on nine reconstruction experiments across biological and synthetic datasets, PACE reduces standard transport distances (MMD, Wasserstein-1/2) by 23.7% on average and improves RNA-velocity alignment by 15.4% without requiring paired cells or lineage tracing during training. Code is released.