Noise-Aware Diffusion for City-Scale Air-Quality Reconstruction from Sparse Monitoring Stations

Reliable air-quality monitoring is essential for urban exposure assessment and environmental policy, yet many downstream applications are hindered by sparse regulatory stations and noisy real-world measurements. While diffusion models have shown promise for probabilistic spatiotemporal imputation, common conditioning strategies can be brittle: purely input-based conditioning may drift from sparse constraints, whereas hard clamping can introduce a clean–noisy mismatch and propagate corrupted readings during reverse sampling. In this work, we propose STGPD (SpatioTemporal Graph Posterior Diffusion), a probabilistic framework that formulates city-scale pollutant reconstruction as posterior sampling on a graph-structured spatiotemporal field. STGPD enforces noise-aware soft consistency by re-noising visible observations to the current diffusion level and fusing a noise-matched measurement term with the model prior via variance-weighted fusion under an explicit observation-noise model. To improve spatial extrapolation in heterogeneous urban environments, we further construct a dual-view graph that combines geographic proximity with functional similarity derived from static descriptors. Experiments on real-world monitoring data in Augsburg, Germany, for PM10 and NO2 show that STGPD provides a robust probabilistic reconstruction framework under extreme sparsity, station outages, and synthetic sensor-noise injection in this sparse-monitoring case study. Compared with strong deterministic and diffusion-based baselines, STGPD achieves improved reconstruction accuracy (MAE/RMSE) and better-calibrated uncertainty estimates (CRPS) under the current evaluation protocols.