# Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models

arXiv: https://arxiv.org/abs/2502.03607 · HTML: https://mlsanity.com/paper/2502.03607/

## Key facts

- Cited by 38 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 22 of its 34 references that are in the map.
- First posted on arXiv 5 Feb 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, 22 of 22)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks](https://mlsanity.com/paper/1906.08291/) (2019)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Motion Planning for Autonomous Driving: The State of the Art and Future Perspectives](https://mlsanity.com/paper/2303.09824/) (2023)
- [Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization](https://mlsanity.com/paper/1707.06618/) (2017)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [EECBS: A Bounded-Suboptimal Search for Multi-Agent Path Finding](https://mlsanity.com/paper/2010.01367/) (2020)
- [Priority Inheritance with Backtracking for Iterative Multi-agent Path Finding](https://mlsanity.com/paper/1901.11282/) (2019)
- [EDMP: Ensemble-of-costs-guided Diffusion for Motion Planning](https://mlsanity.com/paper/2309.11414/) (2023)
- [Potential Based Diffusion Motion Planning](https://mlsanity.com/paper/2407.06169/) (2024)
- [Multi-Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2410.03072/) (2024)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Method](https://mlsanity.com/paper/2110.06365/) (2021)
- [Diffusion Model for Planning: A Systematic Literature Review](https://mlsanity.com/paper/2408.10266/) (2024)
- [Learning Constrained Optimization with Deep Augmented Lagrangian Methods](https://mlsanity.com/paper/2403.03454/) (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, 30 of 38)

- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Constrained Diffusers for Safe Planning and Control](https://mlsanity.com/paper/2506.12544/) (2025)
- [Composition and Alignment of Diffusion Models using Constrained Learning](https://mlsanity.com/paper/2508.19104/) (2025)
- [Discrete-Guided Diffusion for Scalable and Safe Multi-Robot Motion Planning](https://mlsanity.com/paper/2508.20095/) (2025)
- [Projected Coupled Diffusion for Test-Time Constrained Joint Generation](https://mlsanity.com/paper/2508.10531/) (2025)
- [Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generation](https://mlsanity.com/paper/2509.25157/) (2025)
- [Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling](https://mlsanity.com/paper/2505.18017/) (2025)
- [From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies](https://mlsanity.com/paper/2511.06385/) (2025)
- [Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling](https://mlsanity.com/paper/2605.12754/) (2026)
- [Simulation-Informed Diffusion for Decentralized Multi-robot Motion Planning](https://mlsanity.com/paper/2605.27697/) (2026)
- [AL-CoLe: Augmented Lagrangian for Constrained Learning](https://mlsanity.com/paper/2510.20995/) (2025)
- [Improved Constrained Generation by Bridging Pretrained Generative Models](https://mlsanity.com/paper/2603.06742/) (2026)
- [Refining Compositional Diffusion for Reliable Long-Horizon Planning](https://mlsanity.com/paper/2605.03075/) (2026)
- [Inference-Time Attribute Distribution Alignment for Unconditional Diffusion](https://mlsanity.com/paper/2605.07456/) (2026)
- [Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraints](https://mlsanity.com/paper/2605.30825/) (2026)
- [DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising](https://mlsanity.com/paper/2606.15359/) (2026)
- [Scalable Multi Agent Diffusion Policies for Coverage Control](https://mlsanity.com/paper/2509.17244/) (2025)
- [Constrained Diffusion for Accelerated Structure Relaxation of Inorganic Solids with Point Defects](https://mlsanity.com/paper/2602.19153/) (2026)
- [Discrete Diffusion for Complex and Congested Multi-Agent Path Finding with Sparse Social Attention](https://mlsanity.com/paper/2605.13296/) (2026)
- [Motion Planning with Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling](https://mlsanity.com/paper/2607.14455/) (2026)
- [ConEQsA: Concurrent and Asynchronous Embodied Questions Scheduling and Answering](https://mlsanity.com/paper/2509.11663/) (2025)
- [Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization](https://mlsanity.com/paper/2510.09204/) (2025)
- [When Diffusion Breaks Constraints: Sequential Autoregressive Generation with RL and MCTS](https://mlsanity.com/paper/2512.01242/) (2025)
- [Multi-Robot Motion Planning from Vision and Language using Heat-Inspired Diffusion](https://mlsanity.com/paper/2512.13090/) (2025)
- [GenPlanner: From Noise to Plans -- Emergent Reasoning in Flow Matching and Diffusion Models](https://mlsanity.com/paper/2602.18812/) (2026)
- [Train-Small Deploy-Large: Leveraging Diffusion-Based Multi-Robot Planning](https://mlsanity.com/paper/2604.06598/) (2026)
- [Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing](https://mlsanity.com/paper/2604.17838/) (2026)
- [Enforcing Constraints in Generative Sampling via Adaptive Correction Scheduling](https://mlsanity.com/paper/2605.11214/) (2026)
- [NDPP-Grasp: Non-Differentiable Physical Plausibility Constraint-Guided Task-Oriented Dexterous Grasp Generation](https://mlsanity.com/paper/2606.02432/) (2026)
- [Robots as Tokens: Unified Diffusion Transformer for Coordinated Multi-Robot Trajectory Generation](https://mlsanity.com/paper/2606.15550/) (2026)

## Abstract (arXiv)

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address these challenges, this work proposes Simultaneous MRMP Diffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and other learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments.