Title: Energy Guided Geometric Flow Matching
Primary area: generative models
Keywords: flow matching, score matching, geodesic, trajectory inference

Abstract: For temporal data bound to a manifold, a common prior assumes data trajectories also follow this manifold.  Traditional flow matching relies on straight conditional paths, and flow matching methods which learn geodesics rely on RBF kernels or nearest neighbor graphs that suffer from the curse of dimensionality.  We propose to use score matching and annealed energy distillation to learn a metric tensor that captures the underlying data geometry and informs more accurate flows.  We demonstrate the efficacy of this strategy on synthetic manifolds with analytic geodesics, and interpolation of single-cell RNA cell trajectories.

TL;DR: Using score matching and energy distillation as a metric tensor to guide flow matching