Reward Transport: Property Control in Flow Matching via Noise-Space Alignment
We show that this coupling can instead serve as an alignment interface: by matching noise and data according to a target molecular property, it embeds controllable structure directly into the learned flow field. In the coupling-preserving limit, thresholding this coordinate recovers the Cross-Entropy Method's truncated reward distribution, providing a principled, continuously adjustable distribution-level control knob. The interface is complementary to classifier-free guidance and conditional flow matching, while a negative result under epsilon-prediction diffusion clarifies where coupling-level alignment is structurally absent.
- ▪We show that this coupling can instead serve as an alignment interface: by matching noise and data according to a target molecular property, it embeds controllable structure directly into the learned flow field.
- ▪In the coupling-preserving limit, thresholding this coordinate recovers the Cross-Entropy Method's truncated reward distribution, providing a principled, continuously adjustable distribution-level control knob.
- ▪The interface is complementary to classifier-free guidance and conditional flow matching, while a negative result under epsilon-prediction diffusion clarifies where coupling-level alignment is structurally absent.
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Computer Science > Machine Learning arXiv:2607.08781 (cs) [Submitted on 13 Jun 2026] Title:Reward Transport: Property Control in Flow Matching via Noise-Space Alignment Authors:Kehan Guo, Yili Shen, Yujun Zhou, Yue Huang, Chujie Gao, Shiyi Du, Xiangliang Zhang View a PDF of the paper titled Reward Transport: Property Control in Flow Matching via Noise-Space Alignment, by Kehan Guo and 6 other authors View PDF HTML (experimental) Abstract:The coupling in flow matching -- the rule pairing noise vectors with data points -- is typically treated as a computational choice. We show that this coupling can instead serve as an alignment interface: by matching noise and data according to a target molecular property, it embeds controllable structure directly into the learned flow field.
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