# Multi-Agent Path Finding in Continuous Spaces with Projected Diffusion Models

arXiv: https://arxiv.org/abs/2412.17993 · HTML: https://mlsanity.com/paper/2412.17993/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 23 Dec 2024.

## 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, 6 of 6)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Multi-Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2410.03072/) (2024)
- [CTRMs: Learning to Construct Cooperative Timed Roadmaps for Multi-agent Path Planning in Continuous Spaces](https://mlsanity.com/paper/2201.09467/) (2022)

## Built on by (most cited first, 8 of 8)

- [Composition and Alignment of Diffusion Models using Constrained Learning](https://mlsanity.com/paper/2508.19104/) (2025)
- [Where Paths Collide: A Comprehensive Survey of Classic and Learning-Based Multi-Agent Pathfinding](https://mlsanity.com/paper/2505.19219/) (2025)
- [Navigating Motion Agents in Dynamic and Cluttered Environments through LLM Reasoning](https://mlsanity.com/paper/2503.07323/) (2025)
- [Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraints](https://mlsanity.com/paper/2605.30825/) (2026)
- [Motion Planning with Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling](https://mlsanity.com/paper/2607.14455/) (2026)
- [D4orm: Multi-Robot Trajectories with Dynamics-aware Diffusion Denoised Deformations](https://mlsanity.com/paper/2503.12204/) (2025)
- [Multi-robot Path Planning and Scheduling via Model Predictive Optimal Transport (MPC-OT)](https://mlsanity.com/paper/2508.21205/) (2025)
- [Train-Small Deploy-Large: Leveraging Diffusion-Based Multi-Robot Planning](https://mlsanity.com/paper/2604.06598/) (2026)

## Abstract (arXiv)

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared environment poses significant challenges, especially in continuous spaces where traditional optimization algorithms struggle with scalability. Moreover, these algorithms often depend on discretized representations of the environment, which can be impractical in image-based or high-dimensional settings. Recently, diffusion models have shown promise in single-agent path planning, capturing complex trajectory distributions and generating smooth paths that navigate continuous, high-dimensional spaces. However, directly extending diffusion models to MAPF introduces new challenges since these models struggle to ensure constraint feasibility, such as inter-agent collision avoidance. To overcome this limitation, this work proposes a novel approach that integrates constrained optimization with diffusion models for MAPF in continuous spaces. This unique combination directly produces feasible multi-agent trajectories that respect collision avoidance and kinematic constraints. The effectiveness of our approach is demonstrated across various challenging simulated scenarios of varying dimensionality.