# Beyond Transport Cost: Routing Differences between Flow Matching and Optimal Transport

arXiv: https://arxiv.org/abs/2610.05921 · HTML: https://mlsanity.com/paper/2610.05921/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- First posted on arXiv 5 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Abstract (arXiv)

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.