Primal-Dual Flow Matching for Sample-Wise Constrained Generation

Key points

• We consider the problem of learning to generate data while satisfying a prescribed sample-wise constraint with a user-specified probability of constraint satisfaction.1
• 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.1
• We show that PDFM improves constraint satisfaction over vanilla FM and achieves competitive performance against constraint-aware baselines while maintaining distributional fidelity.1

Sources (1)

• [1]Primal-Dual Flow Matching for Sample-Wise Constrained Generation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 08:29 PM

  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 consider the problem of learning to generate data while satisfying a prescribed sample-wise constraint with a user-specified probability of constraint satisfaction.

Extractive summary: sentences quoted from the sources.