Computer Science > Machine Learning
arXiv:2603.09014 (cs)
[Submitted on 9 Mar 2026]
Title:The Coupling Within: Flow Matching via Distilled Normalizing Flows
Authors:David Berthelot, Tianrong Chen, Jiatao Gu, Marco Cuturi, Laurent Dinh, Bhavik Chandna, Michal Klein, Josh Susskind, Shuangfei Zhai
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Abstract:Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of coupling measure for sampling noise/data pairs that define the flow matching (FM) regression loss. While FM training defaults usually to independent coupling, recent works show that adaptive couplings informed by noise/data distributions (e.g., via optimal transport, OT) improve both model training and inference. We radicalize this insight by shifting the paradigm: rather than computing adaptive couplings directly, we use distilled couplings from a different, pretrained model capable of placing noise and data spaces in bijection -- a property intrinsic to normalizing flows (NF) through their maximum likelihood and invertibility requirements. Leveraging recent advances in NF image generation via auto-regressive (AR) blocks, we propose Normalized Flow Matching (NFM), a new method that distills the quasi-deterministic coupling of pretrained NF models to train student flow models. These students achieve the best of both worlds: significantly outperforming flow models trained with independent or even OT couplings, while also improving on the teacher AR-NF model.
| Comments: | |
| Subjects: | Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV) |
| Cite as: | arXiv:2603.09014 [cs.LG] |
| (or arXiv:2603.09014v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.09014
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View a PDF of the paper titled The Coupling Within: Flow Matching via Distilled Normalizing Flows, by David Berthelot and 8 other authors
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