发表机构
The Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对流匹配中轨迹交叉导致的速度场高Lipschitz常数问题，提出CoFlow框架，通过对比学习显式排斥轨迹，降低局部Lipschitz常数，在ImageNet 256x256上少步推理显著降低FID且无额外训练开销。
AI 中文摘要
轨迹交叉仍然是流匹配（FM）中的关键瓶颈，以往的工作通常从理论优化的视角看待这些交叉，导致速度平均化。他们试图通过事后蒸馏或端点耦合来间接解决，而没有显式地调控中间轨迹。在本文中，我们引入了一个新的网络学习视角：交叉点固有地导致目标速度场中的局部Lipschitz常数较大，从而带来两个缺点。首先，高Lipschitz常数对应于速度场中的高频信号，而神经网络由于频谱偏差而难以拟合。其次，它们也意味着剧烈的速度变化，导致少步推理中的严重数值积分误差。为了缓解这一问题，我们提出了CoFlow，一个将对比学习范式引入FM的框架，在训练期间显式地排斥轨迹，从而降低速度场的局部Lipschitz常数。具体来说，我们从随机微分方程（SDE）的角度通过注入排斥漂移项来构建CoFlow。该漂移主动引导正样本的前向过程远离负轨迹，有效降低局部Lipschitz常数。此外，我们从该SDE推导出等价的随机插值公式，为控制负样本的影响提供了简单且易处理的设计空间。在ImageNet 256x256上的大量实验表明，CoFlow在少步推理（例如20步）中相比标准FM显著降低了FID，且没有增加训练开销。代码可在以下网址获取：this https URL
英文摘要
Trajectory crossing remains a critical bottleneck in Flow Matching (FM), and previous works typically view these crossings from a theoretical optimization perspective causing velocity averaging. They attempt to address it indirectly by post-hoc distillation or endpoint coupling, without explicitly regulating the intermediate trajectories. In this paper, we introduce a new network learning perspective: crossing points inherently induce large local Lipschitz constants in the target velocity field, leading to two drawbacks. First, high Lipschitz constants correspond to high-frequency signals in the velocity field that neural networks struggle to fit due to spectral bias. Second, they also imply drastic velocity variations, leading to severe numerical integration errors in few-step inference. To alleviate this, we propose CoFlow, a framework that introduces the contrastive learning paradigm into FM to explicitly repel trajectories during training, thereby lowering the local Lipschitz constants of the velocity field. Specifically, we formulate CoFlow from a Stochastic Differential Equation (SDE) perspective by injecting a repulsive drift term. This drift actively guides the forward process of positive samples away from negative trajectories, effectively reducing the local Lipschitz constant. Furthermore, we derive an equivalent stochastic interpolant formulation from this SDE, providing a simple and tractable design space to control the influence of negative samples. Extensive experiments on ImageNet 256x256 demonstrate that CoFlow significantly reduces FID compared to standard FM in few-step inference (e.g., 20 steps), with no added training overhead. The code can be accessed at: https://github.com/HKUST-LongGroup/CoFlow
Comments18 pages, 5 figures
