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PolyFlow advances the field of constrained generative modeling by embedding safety limits directly into flow dynamics, eliminating post-hoc corrections to ensure zero constraint violation in physical systems. This projection-free architecture significantly reduces inference latency while maintaining high distributional fidelity for planning and control tasks without requiring expensive iterative solvers. The method represents a critical step toward deploying reliable AI agents in safety-critical environments where strict adherence to polyhedral constraints is mandatory.
PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Update
arXiv:2606.13400v1 Announce Type: cross Abstract: While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on https://github.com/MJianM/PolyFlow.
Abstract:While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on this https URL.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Robotics (cs.RO)
arXiv:2606.13400 [cs.LG]
(or arXiv:2606.13400v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.13400 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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