The Velocity Deficit: Initial Energy Injection for Flow Matching
While Flow Matching theoretically guarantees constant-velocity trajectories, we identify a critical breakdown in high-dimensional practice: the Velocity Deficit. We show that the MSE objective systematically underestimates velocity magnitude, causing generated samples to fail to reach the data manifold-a phenomenon we term Integration Lag. To rectify this, we propose Initial Energy Injection, instantiated via two complementary methods: the training-based Magnitude-Aware Flow Matching (MAFM) and the training-free Scale Schedule Corrector (SSC). Both are grounded in our discovery of a crucial asymmetry: velocity contraction causes harmful kinetic stagnation at the trajectory's start, yet ac...
| Authors | Linze Li, Zong-Wei Hong, Shen Zhang et al. |
|---|---|
| Primary category | cs.CV |
| Published | 14 May 2026 |
| Last updated at source | 14 May 2026 |
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