Energy Guided Geometric Flow Matching

ICLR 2026 Conference Submission13214 Authors

Keywords: flow matching, score matching, geodesic, trajectory inference

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

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.

Primary Area: generative models

Submission Number: 13214