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arXiv · 2605.14819

The Velocity Deficit: Initial Energy Injection for Flow Matching

Linze Li·Zong-Wei Hong·Shen Zhang·Bo Lin·Jinglun Li·Yao Tang·Jiajun Liang
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Abstract

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 acts as a beneficial denoising mechanism at its end. Empirically, SSC yields significant efficiency gains with zero retraining and just one line of code. On ImageNet-1k (256x256), it improves FID by 44.6% (from 13.68 to 7.58) and achieves a 5x speedup, enabling a 50-step generator (FID 7.58) to beat a 250-step baseline (FID 8.65). Furthermore, our methods generalize to Text-to-Image tasks and high-resolution generation, improving FID on MS-COCO by ~22%.

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Linze Li, Zong-Wei Hong, Shen Zhang, Bo Lin, Jinglun Li, Yao Tang, Jiajun Liang. 2026-05-14. The Velocity Deficit: Initial Energy Injection for Flow Matching. https://arxiv.org/abs/2605.14819

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