2025/09/25 by Weili Zeng, Yichao Yan, Zeng, Weili +1 · 1 citation
Engineering · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Plasma and Flow Control in Aerodynamics
paper · pdf · doi:10.48550/arxiv.2509.20952
openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.