# Active Learning for Low-Altitude Radio Map Construction via Plug-and-Play Flow Matching

arXiv: https://arxiv.org/abs/2609.27486 · HTML: https://mlsanity.com/paper/2609.27486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 27 of 27)

- [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)
- [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)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2503.08136/) (2025)
- [A Tutorial on Environment-Aware Communications via Channel Knowledge Map for 6G](https://mlsanity.com/paper/2309.07460/) (2023)
- [Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching](https://mlsanity.com/paper/2405.18816/) (2024)
- [Deep Spectrum Cartography: Completing Radio Map Tensors Using Learned Neural Models](https://mlsanity.com/paper/2105.00177/) (2021)
- [Spectrum Surveying: Active Radio Map Estimation with Autonomous UAVs](https://mlsanity.com/paper/2201.04125/) (2022)
- [Propagation Map Reconstruction via Interpolation Assisted Matrix Completion](https://mlsanity.com/paper/2207.13473/) (2022)
- [Integrated Interpolation and Block-term Tensor Decomposition for Spectrum Map Construction](https://mlsanity.com/paper/2402.17138/) (2024)
- [Quantized Radio Map Estimation Using Tensor and Deep Generative Models](https://mlsanity.com/paper/2303.01770/) (2023)
- [Radio-Map-Based Robust Positioning Optimization for UAV-Enabled Wireless Power Transfer](https://mlsanity.com/paper/1905.12394/) (2019)
- [Energy-modified Leverage Sampling for Radio Map Construction via Matrix Completion](https://mlsanity.com/paper/2404.08286/) (2024)
- [Sensing-Enhanced Channel Estimation for Near-Field XL-MIMO Systems](https://mlsanity.com/paper/2403.11809/) (2024)
- [Radio Map Estimation via Latent Domain Plug-and-Play Denoising](https://mlsanity.com/paper/2501.13472/) (2025)
- [Flow Matching-Based Active Learning for Radio Map Construction with Low-Altitude UAVs](https://mlsanity.com/paper/2509.13822/) (2025)
- [Bayesian-Driven Graph Reasoning for Active Radio Map Construction](https://mlsanity.com/paper/2508.09142/) (2025)
- [Predictive Communications for Low-Altitude Networks](https://mlsanity.com/paper/2509.01705/) (2025)

## Abstract (arXiv)

The deployment of unmanned aerial vehicles (UAVs) in low-altitude airspace requires accurate and timely radio maps for reliable communication and safe navigation. However, constructing such radio maps is challenging due to the prohibitive overhead of exhaustive measurements and the limited flight endurance of UAVs. To address this challenge, we propose an active learning framework based on flow matching for efficient low-altitude radio map construction from sparse measurements. We first analyze a plug-and-play (PnP) inference scheme with a flow-matching prior. By characterizing the late-stage refinement behavior through an ordinary differential equation (ODE), we theoretically show how the inference steps smoothly align with a continuous ODE flow to refine the map details. Recognizing that the early generative stages are largely noise-dominated, this insight motivates our proposed truncated flow matching plug-and-play (TFM-PnP) approach. TFM-PnP utilizes a spatial interpolation-based initialization to start the reconstruction from an intermediate flow time, thereby bypassing the inefficient early stages. We further use the generative diversity of flow matching to derive an uncertainty map to guide the UAV trajectory design. Specifically, we propose a weighted sampling approach to select a target location, followed by a Utility-Aware Path Search (UAPS) algorithm to design the corresponding UAV trajectories. Simulation results based on Sionna ray-tracing datasets show that the proposed framework outperforms the considered baselines, achieving more than 50% reduction in normalized mean squared error (NMSE).