The Velocity Deficit: Initial Energy Injection for Flow Matching
For practitioners of generative modeling using flow matching, this work identifies and fixes a fundamental training-inference mismatch that degrades sample quality and efficiency.
Flow Matching suffers from a Velocity Deficit where the MSE objective underestimates velocity magnitude, causing generated samples to miss the data manifold. The proposed Initial Energy Injection methods (MAFM and SSC) correct this, with SSC improving ImageNet-1k FID by 44.6% (from 13.68 to 7.58) and achieving 5x speedup, and generalizing to text-to-image tasks with ~22% FID improvement on MS-COCO.
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%.