Multi-Robot Motion Planning from Vision and Language using Heat-Inspired Diffusion
arXiv:2512.13090v2 Announce Type: replace Abstract: 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 stri