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

Diffusion models achieve high-fidelity radio map construction through iterative denoising, yet their sampling cost limits practicality in dynamic wireless systems where radio maps must be refreshed repeatedly. Meanwhile, classical propagation models encode valuable scene-level knowledge that standard diffusion inference discards entirely by initializing from pure Gaussian noise. This paper bridges propagation priors and diffusion refinement through a mid-start sampling strategy. A matched propagation prior is perturbed to an intermediate diffusion timestep, and the pretrained diffusion backbone executes only the remaining reverse steps, focusing computation on multipath-aware refinement rather than full reconstruction from noise. We provide theoretical analysis establishing an upper bound on the initialization gap, a sufficient condition under which truncation improves reconstruction fidelity, and a formal characterization of prior-quality sensitivity under aggressive truncation. Experiments on IRT4HighRes show that, at $P_{\text{start}}=0.5$, the proposed method achieves a $2.01\times$ speedup while simultaneously improving NMSE, RMSE, SSIM, and PSNR over the full-step baseline. A prior-quality ablation across three propagation models of different fidelity confirms that reconstruction quality tracks prior quality, with the sensitivity amplified under shorter reverse trajectories, consistent with the theoretical predictions. These results also suggest that mid-start reconstruction quality can serve as a proxy for ranking the scene-level fidelity of different propagation models.

Fine-scale rainfall reconstruction is critical for urban flood modeling, but real rainfall sensing systems observe the field through incompatible spatial supports: gauges measure points, microwave links measure paths, and radar/satellite products measure gridded areas. These differences in measurement support impose geometrically distinct constraints on the rainfall field, yet existing heterogeneous graph approaches reconcile such sources in feature space, giving each its own embedding while discarding the geometry of its support. We propose a geometry-aware multi-support heterogeneous graph neural network that represents each observation according to its support type (0D point, 1D line, or 2D grid) as a distinct node layer, and fuses them through cross-support message passing into a point-support prediction layer from which the field is reconstructed. An inductive masked-node formulation decouples prediction resolution from sensing resolution, allowing the same trained model to reconstruct the field at user-defined target locations or display grids. On Singapore data, the proposed method reduces RMSE by 23.2% over the classical interpolation baseline, inverse-distance weighting, and consistently outperforms other neural architectures such as convolutional fusion and support-agnostic heterogeneous graph baselines. A generalization study using data from Sydney, Australia lets us characterize when multi-support fusion helps: the available skill appears to depend on gauge spacing relative to the spatial correlation length of the field, so fusion delivers the largest gains where the field is under-sampled relative to its correlation length and little when it is already resolved. Code and models will be open-sourced upon paper acceptance.

High-resolution rainfall observations are crucial for weather forecasting, water management, and hazard mitigation. Traditional operational measurements are often biased and low-resolution, limiting their ability to capture local rainfall. Accurate high-resolution rainfall maps require integrating sparse surface observations, yet existing deep learning densification methods are hindered by rainfall's skewed, localized nature, noise, and limited spatio-temporal fusion. We present DropsToGrid, a Neural Process-based method that generates dense rainfall fields by fusing temporal sequences from noisy, irregularly distributed private weather stations with spatial context from radar. Leveraging multi-scale feature extraction, temporal attention, and multi-modal fusion, the model produces stochastic, continuous rainfall estimates and explicitly quantifies uncertainty. Evaluations on real-world datasets demonstrate that DropsToGrid outperforms both operational and deep learning baselines, generating accurate high-resolution rainfall maps with well-calibrated uncertainty, even when only few stations are available and in cross-regional scenarios.