# Multi-Robot Motion Planning from Vision and Language using Heat-Inspired Diffusion

arXiv: https://arxiv.org/abs/2512.13090 · HTML: https://mlsanity.com/paper/2512.13090/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 24 of 24)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [CLIPort: What and Where Pathways for Robotic Manipulation](https://mlsanity.com/paper/2109.12098/) (2021)
- [CoWs on Pasture: Baselines and Benchmarks for Language-Driven Zero-Shot Object Navigation](https://mlsanity.com/paper/2203.10421/) (2022)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Multimodal Diffusion Transformer: Learning Versatile Behavior from Multimodal Goals](https://mlsanity.com/paper/2407.05996/) (2024)
- [EECBS: A Bounded-Suboptimal Search for Multi-Agent Path Finding](https://mlsanity.com/paper/2010.01367/) (2020)
- [ManiFlow: A General Robot Manipulation Policy via Consistency Flow Training](https://mlsanity.com/paper/2509.01819/) (2025)
- [Multi-Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2410.03072/) (2024)
- [Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models](https://mlsanity.com/paper/2502.03607/) (2025)
- [AC-DiT: Adaptive Coordination Diffusion Transformer for Mobile Manipulation](https://mlsanity.com/paper/2507.01961/) (2025)
- [LTLDoG: Satisfying Temporally-Extended Symbolic Constraints for Safe Diffusion-based Planning](https://mlsanity.com/paper/2405.04235/) (2024)
- [Denoising Heat-inspired Diffusion with Insulators for Collision Free Motion Planning](https://mlsanity.com/paper/2310.12609/) (2023)
- [Efficient Multi-Agent Trajectory Planning with Feasibility Guarantee using Relative Bernstein Polynomial](https://mlsanity.com/paper/1909.10219/) (2019)
- [Transporting Robotic Swarms via Mean-Field Feedback Control](https://mlsanity.com/paper/2006.11462/) (2020)

## Abstract (arXiv)

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/