The Velocity Deficit: Initial Energy Injection for Flow Matching
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911685719097344 |
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| author | Li, Linze Hong, Zong-Wei Zhang, Shen Lin, Bo Li, Jinglun Tang, Yao Liang, Jiajun |
| author_facet | Li, Linze Hong, Zong-Wei Zhang, Shen Lin, Bo Li, Jinglun Tang, Yao Liang, Jiajun |
| contents | 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%. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14819 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Velocity Deficit: Initial Energy Injection for Flow Matching Li, Linze Hong, Zong-Wei Zhang, Shen Lin, Bo Li, Jinglun Tang, Yao Liang, Jiajun Computer Vision and Pattern Recognition 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%. |
| title | The Velocity Deficit: Initial Energy Injection for Flow Matching |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2605.14819 |