Primal-Dual Flow Matching for Sample-Wise Constrained Generation
Read the original on arXiv Machine Learning →The paper introduces Primal-Dual Flow Matching (PDFM), a method for learning data generators that satisfy user‑specified sample‑wise constraints with a guaranteed probability of satisfaction. PDFM builds on a population‑level constrained negative log‑likelihood objective and a flow‑matching parameterization, providing theoretical guarantees under regularity and expressivity assumptions. Practically, PDFM requires only binary membership oracle feedback, avoids differentiable distance metrics or convexity assumptions, and empirically outperforms vanilla flow matching while maintaining distributional fidelity.
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