Energy Guided Geometric Flow Matching
This work addresses the challenge of improving flow matching methods for temporal data by mitigating the curse of dimensionality in geometric learning, though it appears incremental as it builds on existing flow matching and score matching techniques.
The paper tackled the problem of learning accurate flows for temporal data by proposing a method that uses score matching and annealed energy distillation to learn a metric tensor capturing data geometry, demonstrating efficacy on synthetic manifolds with analytic geodesics and cell interpolation.
A useful inductive bias for temporal data is that trajectories should stay close to the data 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 faithfully 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 cell