Generative Bayesian Spectrum Cartography: Unified Reconstruction and Active Sensing via Diffusion Models

High-fidelity spectrum cartography is pivotal for spectrum management and wireless situational awareness, yet it remains a challenging ill-posed inverse problem due to the sparsity and irregularity of observations. Furthermore, existing approaches often decouple reconstruction from sensing, lacking a principled mechanism for informative sampling. To address these limitations, this paper proposes a unified diffusion-based Bayesian framework that jointly addresses spectrum reconstruction and active sensing. We formulate the reconstruction task as a conditional generation process driven by a learned diffusion prior. Specifically, we derive tractable, closed-form posterior transition kernels for the reverse diffusion process, which enforce consistency with both linear Gaussian and non-linear quantized measurements. Leveraging the intrinsic probabilistic nature of diffusion models, we further develop an uncertainty-aware active sampling strategy. This strategy quantifies reconstruction uncertainty to adaptively guide sensing agents toward the most informative locations, thereby maximizing spectral efficiency. Extensive experiments demonstrate that the proposed framework significantly outperforms state-of-the-art interpolation, sparsity-based, and deep learning baselines in terms of reconstruction accuracy, sampling efficiency, and robustness to low-bit quantization.