The Velocity Deficit: Initial Energy Injection for Flow Matching
Linze Li, Zong-Wei Hong, Shen Zhang, Bo Lin, Jinglun Li, Yao Tang, Jiajun Liang
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%.
BibTeX
@inproceedings{
li2026the,
title={The Velocity Deficit: Initial Energy Injection for Flow Matching},
author={Linze Li and Zong-Wei Hong and Shen Zhang and Bo Lin and Jinglun Li and Yao Tang and Jiajun Liang},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=ddBkQ4koaI}
}