The Coupling Within: Flow Matching via Distilled Normalizing Flows

• URL: http://arxiv.org/abs/2603.09014v1
• Date: Mon, 09 Mar 2026 23:07:36 GMT
• Title: The Coupling Within: Flow Matching via Distilled Normalizing Flows
• Abstract summary: A crucial ingredient in flow training is the choice of coupling measure for sampling noise/data pairs.<n>We propose Normalized Flow Matching, a new method that distills the quasi-deterministic coupling of pretrained NF models to train student flow models.
• Score: 45.3372883861006
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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