Primal-Dual Flow Matching for Sample-Wise Constrained Generation
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Computer Science > Machine Learning
Title:Primal-Dual Flow Matching for Sample-Wise Constrained Generation
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)
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