# Discrete-Guided Diffusion for Scalable and Safe Multi-Robot Motion Planning

## TL;DR

This paper introduces Discrete-Guided Diffusion, a novel framework that combines discrete MAPF and diffusion models to enable scalable, high-quality multi-robot motion planning in large environments.

## Contribution

It presents a new integrated approach that decomposes MRMP into convex subproblems, guiding diffusion models with discrete solutions for improved scalability and trajectory quality.

## Key findings

- Scales to 100 robots in complex environments
- Achieves high success rates and planning efficiency
- Sets new state-of-the-art performance in large-scale MRMP

## Abstract

Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their scalability, their coarse discretization severely limits trajectory quality. In contrast, continuous optimization-based planners offer higher-quality paths but suffer from the curse of dimensionality, resulting in poor scalability with respect to the number of robots. This paper tackles the limitations of these two approaches by introducing a novel framework that integrates discrete MAPF solvers with constrained generative diffusion models. The resulting framework, called Discrete-Guided Diffusion (DGD), has three key characteristics: (1) it decomposes the original nonconvex MRMP problem into tractable subproblems with convex configuration spaces, (2) it combines discrete MAPF solutions with constrained optimization techniques to guide diffusion models capture complex spatiotemporal dependencies among robots, and (3) it incorporates a lightweight constraint repair mechanism to ensure trajectory feasibility. The proposed method sets a new state-of-the-art performance in large-scale, complex environments, scaling to 100 robots while achieving planning efficiency and high success rates.