Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors

Commercial Microwave Links (CMLs) offer dense spatial coverage for rainfall sensing but produce path-integrated measurements that make accurate ground-level reconstruction challenging. Existing methods typically oversimplify CMLs as point sensors and neglect the physical power-law relating rainfall to signal attenuation, resulting in degraded performance under heterogeneous precipitation. In this work, we view rain field reconstruction as a Bayesian inverse problem with Diffusion Models (DMs) as high-fidelity spatial priors. We show that diffusion models better preserve key rainfall statistics compared to censored Gaussian processes. Framing rainfall estimation as a Bayesian inverse problem with a DM prior enables training-free posterior sampling using a broad family of methods, including Plug-and-Play, Sequential Monte Carlo, and Replica Exchange methods. Experiments on synthetic and real-world datasets demonstrate consistent improvements over established CML-based reconstruction baselines.

Accurate local rainfall maps are essential for flood warnings and water management, but traditional sensors each have gaps: rain gauges are sparse, radar can be noisy, and satellites are often too coarse. This paper studies how to reuse commercial microwave links, the radio signals already used in cellular networks, as dense near-ground rain sensors. Rain weakens microwave signals along each link, but each signal reports only the total effect over a whole path, so many different rainfall maps could explain the same measurements. We address this ambiguity as a probabilistic reconstruction problem, combining a physics-based model of how rain affects each link with a diffusion model, a model trained to generate realistic rainfall patterns. The method can produce plausible rain fields without retraining the diffusion model for each new measurement setup, and it can represent uncertainty rather than returning only one rainfall map. Experiments on simulated data and on the OpenMRG dataset from Gothenburg show that these diffusion-based reconstructions generally match reference rainfall maps better than established interpolation methods that treat each link like a point sensor. This suggests that existing telecommunication infrastructure could help deliver more detailed, affordable rainfall monitoring where dedicated sensors are sparse.