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

2026-06-11

AI Summary

This work addresses the challenge of efficiently generating samples that strictly satisfy polyhedral constraints in safety-critical physical systems, where existing flow-based generative models either fail to enforce such constraints or rely on computationally expensive post-processing that often distorts the learned distribution. To overcome these limitations, the authors propose PolyFlow, a novel framework that, for the first time, directly embeds arbitrary linear inequality constraints into both the dynamics and neural architecture of discrete-time flow matching. This integration ensures exact satisfaction of polyhedral constraints without requiring projection or post-hoc correction, while also eliminating discretization errors. Empirical results demonstrate that PolyFlow achieves zero constraint violations across diverse planning and control tasks, maintains high distributional fidelity, and exhibits significantly lower inference latency compared to current state-of-the-art methods.

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.

Problem

• flow-based generative models
• safety-critical systems
• polytope-constrained generation
• constraint satisfaction
• distributional fidelity

Innovation

• polytope-constrained flow matching
• constraint embedding
• projection-free update
• discrete-time flow
• safe generative modeling