发表机构
School of Integrated Technology, Yonsei University（延世大学综合技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过分离传输成本与路由，证明流匹配与最优传输在路由上可不同而成本相近，并提出路由感知耦合以改进生成，强调成本与路由共同评估耦合设计。
AI 中文摘要
在生成模型中，最优传输（OT）被用于通过降低噪声-数据耦合成本来改进流匹配（FM）。然而，不同的噪声到输出分配可能产生几乎相等的成本，这引发了一个关键问题：成本本身是否足以指导耦合设计？我们通过将传输成本与路由（即每个噪声样本所到达的目的地）分离来解决这个问题。我们数值上展示了FM和OT在路由上可能不同，同时成本保持接近。我们考察了这在学习神经FM中的后果。使用精确的FM路由作为预言机，我们进一步构建了一种路由感知的训练耦合，并发现与成本匹配、仅考虑成本的对应物相比，它在生成方面产生了一致的方向性改进。我们的发现强调了成本最小化可能忽视的内容，并促使使用成本和路由来评估基于OT的FM耦合的设计。代码将在论文被接收后发布。
英文摘要
In generative models, Optimal Transport (OT) is used to improve Flow Matching (FM) by reducing noise-data coupling cost. However, different noise-to-output assignments can yield nearly equal costs, raising a key question. Is cost alone sufficient to guide coupling design? We address this question by separating transport cost from routing, i.e., the destination reached by each noise sample. We show numerically how FM and OT can differ in routing while remaining close in cost. We examine its consequences in learned neural FM. Using the exact FM routing as an oracle, we further construct a routing-aware training coupling and find that it yields a directionally consistent improvement in generation over a cost-matched, cost-only counterpart. Our findings highlight what cost minimization can overlook and motivate using both cost and routing to evaluate the design of OT-based FM couplings. Code will be released upon acceptance.
