Beyond Transport Cost: Routing Differences between Flow Matching and Optimal Transport
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 gener...
| Authors | Eungyeol Han, Jong-Seok Lee |
|---|---|
| Primary category | cs.LG |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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