# Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization

arXiv: https://arxiv.org/abs/2510.09204 · HTML: https://mlsanity.com/paper/2510.09204/

## 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 30 of its 53 references that are in the map.
- First posted on arXiv 10 Oct 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, 30 of 30)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints](https://mlsanity.com/paper/2506.04171/) (2025)
- [EDMP: Ensemble-of-costs-guided Diffusion for Motion Planning](https://mlsanity.com/paper/2309.11414/) (2023)
- [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)
- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Transformer-based Model Predictive Control: Trajectory Optimization via Sequence Modeling](https://mlsanity.com/paper/2410.23916/) (2024)
- [B-GAP: Behavior-Rich Simulation and Navigation for Autonomous Driving](https://mlsanity.com/paper/2011.03748/) (2020)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [Online Trajectory Generation with Distributed Model Predictive Control for Multi-Robot Motion Planning](https://mlsanity.com/paper/1909.05150/) (2019)
- [Interactive Joint Planning for Autonomous Vehicles](https://mlsanity.com/paper/2310.18301/) (2023)
- [PILOT: Efficient Planning by Imitation Learning and Optimisation for Safe Autonomous Driving](https://mlsanity.com/paper/2011.00509/) (2020)
- [Decentralized iLQR for Cooperative Trajectory Planning of Connected Autonomous Vehicles via Dual Consensus ADMM](https://mlsanity.com/paper/2301.04386/) (2023)
- [A Survey of Distributed Optimization Methods for Multi-Robot Systems](https://mlsanity.com/paper/2103.12840/) (2021)
- [Efficient Multi-Agent Trajectory Planning with Feasibility Guarantee using Relative Bernstein Polynomial](https://mlsanity.com/paper/1909.10219/) (2019)
- [DeepMNavigate: Deep Reinforced Multi-Robot Navigation Unifying Local & Global Collision Avoidance](https://mlsanity.com/paper/1910.09441/) (2019)
- [Distributed Differential Dynamic Programming Architectures for Large-Scale Multi-Agent Control](https://mlsanity.com/paper/2207.13255/) (2022)
- [AMSwarm: An Alternating Minimization Approach for Safe Motion Planning of Quadrotor Swarms in Cluttered Environments](https://mlsanity.com/paper/2303.04856/) (2023)
- [The Holy Grail of Multi-Robot Planning: Learning to Generate Online-Scalable Solutions from Offline-Optimal Experts](https://mlsanity.com/paper/2107.12254/) (2021)
- [Heter-Sim: Heterogeneous multi-agent systems simulation by interactive data-driven optimization](https://mlsanity.com/paper/1812.00307/) (2018)
- [Robust Multi-Robot Trajectory Optimization Using Alternating Direction Method of Multiplier](https://mlsanity.com/paper/2111.07016/) (2021)
- [Event-triggered and distributed model predictive control for guaranteed collision avoidance in UAV swarms](https://mlsanity.com/paper/2206.11020/) (2022)
- [SRL-ORCA: A Socially Aware Multi-Agent Mapless Navigation Algorithm In Complex Dynamic Scenes](https://mlsanity.com/paper/2306.10477/) (2023)
- [Learning Sampling Distribution and Safety Filter for Autonomous Driving with VQ-VAE and Differentiable Optimization](https://mlsanity.com/paper/2403.19461/) (2024)
- [A message-passing algorithm for multi-agent trajectory planning](https://mlsanity.com/paper/1311.4527/) (2013)
- [GPU Accelerated Convex Approximations for Fast Multi-Agent Trajectory Optimization](https://mlsanity.com/paper/2011.04240/) (2020)

## Abstract (arXiv)

Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often computationally intractable beyond a very small swarm size. In this paper, we propose Flow-Opt, a learning-based approach towards improving the computational tractability of centralized multi-robot trajectory optimization. Specifically, we reduce the problem to first learning a generative model to sample different candidate trajectories and then using a learned Safety-Filter(SF) to ensure fast inference-time constraint satisfaction. We propose a flow-matching model with a diffusion transformer (DiT) augmented with permutation invariant robot position and map encoders as the generative model. We develop a custom solver for our SF and equip it with a neural network that predicts context-specific initialization. The initialization network is trained in a self-supervised manner, taking advantage of the differentiability of the SF solver. We advance the state-of-the-art in the following respects. First, we show that we can generate trajectories of tens of robots in cluttered environments in a few tens of milliseconds. This is several times faster than existing centralized optimization approaches. Moreover, our approach also generates smoother trajectories orders of magnitude faster than competing baselines based on diffusion models. Second, each component of our approach can be batched, allowing us to solve a few tens of problem instances in a fraction of a second. We believe this is a first such result; no existing approach provides such capabilities. Finally, our approach can generate a diverse set of trajectories between a given set of start and goal locations, which can capture different collision-avoidance behaviors.