PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Update

PolyFlow is a novel polytope-constrained flow matching framework that integrates constraints directly into the model and flow dynamics, eliminating the need for post-hoc corrections. It features a discrete-time flow formulation and a projection-free architecture, ensuring zero constraint violation while maintaining high distributional fidelity in planning and control tasks. This approach significantly reduces inference latency compared to existing constrained generation methods, making it a valuable tool for practitioners working with safety-critical applications in flow-based generative models.