The Velocity Deficit: Initial Energy Injection for Flow Matching

TL;DR

This paper identifies a velocity underestimation issue in flow matching for high-dimensional data, and proposes initial energy injection methods, notably SSC, to improve efficiency and quality in image generation tasks.

Contribution

The paper introduces Initial Energy Injection techniques, including SSC, to address velocity contraction issues and enhance flow matching performance without retraining.

Findings

SSC improves FID by 44.6% on ImageNet-1k.

SSC achieves a 5x speedup in generation.

Methods generalize to Text-to-Image and high-res tasks.

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%.