Diffusion models have recently emerged as powerful tools for robot motion planning by capturing the multi-modal distribution of feasible trajectories. However, their extension to multi-robot settings with flexible, language-conditioned task specifications remains limited. Furthermore, current diffusion-based approaches incur high computational cost during inference and struggle with generalization because they require explicit construction of environment representations and lack mechanisms for reasoning about geometric reachability. To address these limitations, we present Language-conditioned Heat-inspired Diffusion (LHD), an end-to-end vision-based framework that generates language-conditioned, collision-free trajectories. LHD integrates semantic priors from CLIP, a vision-language model (VLM), with a collision-avoiding diffusion kernel serving as a physical inductive bias that enables the planner to interpret language commands strictly within the reachable workspace. This naturally handles out-of-distribution (OOD) scenarios -- in terms of reachability -- by guiding robots toward accessible alternatives that match the semantic intent, while eliminating the need for explicit obstacle information at inference time. Extensive evaluations on diverse real-world-inspired maps, along with real-robot experiments, show that LHD consistently outperforms prior diffusion-based planners in success rate, while reducing planning latency. Project page is available at: https://jebeom.github.io/lhd_project_page/

翻译：扩散模型近期通过捕捉可行轨迹的多模态分布，已成为机器人运动规划的有力工具。然而，其向具有灵活语言条件任务规范的多机器人场景的扩展仍十分有限。此外，现有基于扩散的方法在推理过程中计算成本高昂，且由于需要显式构建环境表征、缺乏几何可达性推理机制，难以实现泛化。为解决这些局限性，我们提出了语言条件热启发扩散（LHD），一种端到端的基于视觉的框架，可生成符合语言约束的无碰撞轨迹。LHD将来自视觉-语言模型（VLM）CLIP的语义先验与作为物理归纳偏置的避碰扩散核相结合，使规划器能够严格在可达工作空间内解释语言指令。该方法通过引导机器人转向符合语义意图的可达替代方案，自然处理了与可达性相关的分布外（OOD）场景，同时消除了推理时对显式障碍物信息的需求。在多种真实世界启发地图上的广泛评估及真实机器人实验表明，LHD在成功率上始终优于先前基于扩散的规划器，同时减少了规划延迟。项目页面见：https://jebeom.github.io/lhd_project_page/