让生成模型严格满足复杂约束，且速度更快、不扭曲分布。
PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Update
- 将约束嵌入模型动态，用无投影更新避免迭代求解
- 零约束违反，生成分布保真度高，推理延迟显著降低
- 适合机器人规划、自动驾驶等安全关键场景
基于流的生成模型在多个领域表现优异，但在安全关键物理系统中部署仍具挑战，因需严格满足约束条件。现有方法通常通过事后修正实现安全，带来巨大计算开销并可能扭曲学习到的分布。我们提出 PolyFlow，一种多面体约束下的流匹配框架，将约束直接嵌入模型和流动力学中。PolyFlow 采用离散时间流公式和无投影架构，消除离散化误差，确保任意多面体约束严格满足，无需昂贵的迭代求解器。实验表明，PolyFlow 在各类规划与控制任务中实现零约束违反，同时保持高分布保真度。相比最先进约束生成基线，PolyFlow 显著降低推理延迟，并在安全性、效率与生成质量间取得良好权衡。代码已开源：https://github.com/MJianM/PolyFlow。
原文摘要 · Abstract (English)
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.
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