发表机构
University of California, Irvine; University of North Carolina at Chapel Hill（加州大学尔湾分校; 北卡罗来纳大学教堂山分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出DeGG-Flow框架，将多智能体生成建模为控制仿射动力系统，为共享和私有两类耦合要求建立可行性条件与收敛保证，并推导Wasserstein界，实现满足硬约束的多智能体生成。
AI 中文摘要
生成建模被广泛用于从复杂的多模态分布中生成多样化的对象。然而，其表达能力通常不带有正式保证，即生成的对象满足硬约束或要求。在多智能体生成中，这一问题变得更加具有挑战性，因为一个硬要求可能依赖于多个智能体，而每个智能体可能需要在不依赖其他智能体同时计算的引导输入的情况下，确定自己的引导输入。为此，我们提出了DeGG-Flow，一个用于多智能体流匹配与解耦生成引导的通用框架。通过将生成过程表示为控制仿射动力系统，我们为两类耦合要求开发了引导条件：共享要求，其满足依赖于多个智能体共同作用；以及私有要求，与每个个体智能体相关联并依赖于其邻居。对于这两类要求，我们建立了可行性条件和有限时域收敛保证。我们进一步推导了一个Wasserstein界，用以刻画由引导引起的分布偏差。我们在多机器人协作跨越空间间隙并通过重构环境，以及具有可供性要求的多对象场景生成上展示了DeGG-Flow。在这两个应用中，DeGG-Flow直接生成满足所有相应硬要求的对象，包括在训练中未见过的团队规模。
英文摘要
Generative modeling is widely used for producing diverse objects from complex, multimodal distributions. However, its expressivity does not, in general, come with formal guarantees that the generated objects satisfy hard constraints or requirements. In multi-agent generation, this problem becomes more challenging because a hard requirement can depend on multiple agents, while each agent may need to determine its own guidance input without relying on the simultaneously computed guidance inputs of other agents. To this end, we introduce DeGG-Flow, a general framework for multi-agent flow matching with decoupled generative guidance. By representing the generative process as a control-affine dynamical system, we develop guidance conditions for two classes of coupled requirements: shared requirements whose satisfaction depends on multiple agents together, and private requirements associated with each individual agent dependent on its neighbors. For both classes, we establish feasibility conditions and finite-horizon convergence guarantees. We further derive a Wasserstein bound that characterizes the distributional deviation induced by the guidance. We demonstrate DeGG-Flow on multi-robot collaboration for crossing a spatial gap by reconfiguring the environment, and on multi-object scene generation with affordance requirements. Across both applications, DeGG-Flow directly generates objects that satisfy all corresponding hard requirements, including at team sizes unseen during training.
