让扩散模型在不重训练的情况下安全规划，通过约束采样实现轨迹合规。
Constrained Diffusers for Safe Planning and Control
- 用约束朗之万采样法改进反向扩散过程，直接融入安全约束。
- 在多个任务中满足约束且计算更快，静态与动态环境均有效。
- 适合需要实时安全控制的机器人、自动驾驶等场景。
扩散模型在规划与控制任务中展现出强大潜力，能表示动作与轨迹的多模态分布。然而，确保约束下的安全性仍是关键挑战。本文提出无需重训练或修改架构的约束扩散模型（Constrained Diffusers），借鉴约束优化思想，采用约束朗之万采样机制，在反向扩散过程中联合优化轨迹并满足约束，通过投影法、原对偶法和增广拉格朗日法三种迭代算法实现。此外，引入离散控制屏障函数作为约束，保障在线实施时的安全性。在Maze2D、运动控制及PyBullet球跑任务中的实验表明，该方法在满足约束的同时计算开销更低，且在静态与时变约束环境下表现优于现有方法。
原文摘要 · Abstract (English)
Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge for diffusion models. This paper proposes Constrained Diffusers, a novel framework that incorporates constraints into pre-trained diffusion models without retraining or architectural modifications. Inspired by constrained optimization, we apply a constrained Langevin sampling mechanism for the reverse diffusion process that jointly optimizes the trajectory and realizes constraint satisfaction through three iterative algorithms: projected method, primal-dual method and augmented Lagrangian approaches. In addition, we incorporate discrete control barrier functions as constraints for constrained diffusers to guarantee safety in online implementation. Experiments in Maze2D, locomotion, and pybullet ball running tasks demonstrate that our proposed methods achieve constraint satisfaction with less computation time, and are competitive to existing methods in environments with static and time-varying constraints.
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