arXiv：cs.LG· Zhengyan Huan, Peter Y. Lu, Shuchin Aeron·· 11 小时前
Primal-Dual Flow Matching：样本级约束生成新方法
Primal-Dual Flow Matching for Sample-Wise Constrained Generation
AI 导读
研究者提出 Primal-Dual Flow Matching（PDFM），在流匹配框架下实现样本级约束生成，可直接控制约束满足率，且仅需二元成员查询反馈，无需可微距离、投影或约束集凸性等特殊结构。PDFM 的约束满足表现优于原始 FM，并在保持分布保真度上与约束感知基线具竞争力。该工作已被 NeurIPS 2026 接收，代码已开源。
正文
Abstract:We consider the problem of learning to generate data while satisfying a prescribed \emph{sample-wise} constraint with a user-specified probability of constraint satisfaction. Starting with a population-level constrained negative log-likelihood minimization and using a flow-matching (FM) parameterization, under regularity assumptions and sufficient expressivity of the velocity field family, we derive guarantees on the probability of constraint satisfaction for the corresponding primal-dual optimization algorithm. We provide a practical implementation of this approach, called Primal-Dual Flow Matching (PDFM), which has direct control over constraint satisfaction rate and requires only binary membership oracle feedback for constraint satisfaction, avoiding the need for differentiable distances, projections, or special structure of the constraint set, such as convexity. We show that PDFM improves constraint satisfaction over vanilla FM and achieves competitive performance against constraint-aware baselines while maintaining distributional fidelity. Our code is available at this https URL.
| Comments: | Accepted at NeurIPS 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12699 [cs.LG] |
| (or arXiv:2610.12699v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12699 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Zhengyan Huan [view email]
[v1]
Thu, 8 Oct 2026 20:29:45 UTC (2,778 KB)
来源：arXiv：cs.LG · arxiv.org