aiqbench analysis
This paper studies how to pair source and target samples when training flow-matching generative models, and finds that more optimal-transport-like couplings don't reliably improve sample quality, especially when only a few function evaluations are allowed. ReCouple uses coarse-grained couplings to make that trade-off controllable, with extensions toward continuous sources and spatial regularization. For practitioners, the useful takeaway is that coupling optimality has to be balanced against the network's capacity and the inference budget, not maximized on its own.
Coarse-Graining Optimal Transport for Rollout-Free Post-Training of Flow Matching
arXiv:2610.41269v1 Announce Type: cross Abstract: Flow matching depends critically on the coupling used to pair source and target samples. Optimal transport (OT) couplings can reduce velocity conflict and straighten trajectories; but, in practice, challenges remain: the source comes from a continuous distribution, only a finite number of target samples data are accessible, and the neural network has finite capacity. For these reasons, making the coupling more OT-like may not consistently improve sampling quality, in particular in the low number-of-function-evaluation (NFE) regime. Motivated by this, we introduce ReCouple, a controllable framework that constructs coarse-grained OT couplings, to better understand rollout-free OT-based post-training. We also consider extensions of this basic framework: ReCouple+ extends this toward the continuous-source setting by increasing source resolution, converging to semi-discrete OT in the appropriate limit; and ReCouple++ further adds spatial regularization, motivated by the observation that straight trajectories need not correspond to spatially simple velocity fields. Empirical validation demonstrates the effectiveness of these methods, and it reveals an NFE-dependent interplay between coupling optimality, neural realizability, and generation quality.
Abstract:Flow matching depends critically on the coupling used to pair source and target samples. Optimal transport (OT) couplings can reduce velocity conflict and straighten trajectories; but, in practice, challenges remain: the source comes from a continuous distribution, only a finite number of target samples data are accessible, and the neural network has finite capacity. For these reasons, making the coupling more OT-like may not consistently improve sampling quality, in particular in the low number-of-function-evaluation (NFE) regime. Motivated by this, we introduce ReCouple, a controllable framework that constructs coarse-grained OT couplings, to better understand rollout-free OT-based post-training. We also consider extensions of this basic framework: ReCouple+ extends this toward the continuous-source setting by increasing source resolution, converging to semi-discrete OT in the appropriate limit; and ReCouple++ further adds spatial regularization, motivated by the observation that straight trajectories need not correspond to spatially simple velocity fields. Empirical validation demonstrates the effectiveness of these methods, and it reveals an NFE-dependent interplay between coupling optimality, neural realizability, and generation quality.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.41269 [stat.ML]
(or arXiv:2610.41269v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.41269 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 263 words