# PIER-Flow: Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation

arXiv: https://arxiv.org/abs/2607.10288 · HTML: https://mlsanity.com/paper/2607.10288/

## 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 17 of its 26 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## 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, 17 of 17)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [Consistency Models as a Rich and Efficient Policy Class for Reinforcement Learning](https://mlsanity.com/paper/2309.16984/) (2023)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Where to go next: Learning a Subgoal Recommendation Policy for Navigation Among Pedestrians](https://mlsanity.com/paper/2102.13073/) (2021)
- [Model Predictive Contouring Control for Collision Avoidance in Unstructured Dynamic Environments](https://mlsanity.com/paper/2010.10190/) (2020)
- [A Comprehensive Review on Autonomous Navigation](https://mlsanity.com/paper/2212.12808/) (2022)
- [LDP: A Local Diffusion Planner for Efficient Robot Navigation and Collision Avoidance](https://mlsanity.com/paper/2407.01950/) (2024)
- [Safe, Task-Consistent Manipulation with Operational Space Control Barrier Functions](https://mlsanity.com/paper/2503.06736/) (2025)
- [ALGAMES: A Fast Solver for Constrained Dynamic Games](https://mlsanity.com/paper/1910.09713/) (2019)

## Abstract (arXiv)

Autonomous navigation in dense and highly dynamic environments requires both physically feasible control and low-latency replanning. Optimization-based methods such as Model Predictive Control (MPC) explicitly handle robot kinematics and safety constraints, but repeated nonlinear optimization can limit real-time responsiveness. Deterministic behavior-cloning policies enable efficient inference but may fail to represent multimodal avoidance behaviors, whereas diffusion policies capture multimodality at the cost of time-consuming iterative denoising. We propose PIER-Flow (Physics-Informed Efficient Rectified Flow), a lightweight navigation policy for mobile robots. By distilling an MPC expert into a continuous-time Ordinary Differential Equation (ODE), PIER-Flow achieves single-step action generation through parallel latent sampling and lightweight feasibility selection. We introduce a physics-informed training objective to enforce kinematic consistency, paired with an asynchronous action chunking architecture for robust sim-to-real deployment. Extensive simulations demonstrate that PIER-Flow achieves a 98.85% success rate and zero collisions, with an average inference of ~1.29 ms, which accelerates planning by 37.2× compared to MPC and over 800× against standard diffusion models. Crucially, real-world deployment on a resource-constrained edge computer further achieves an approximately stable inference latency of ~5.3 ms, avoiding the latency spikes and freezing events observed with planning baselines.