RadioDiff-Inverse: Diffusion Enhanced Bayesian Inverse Estimation for ISAC Radio Map Construction

Radio maps (RMs) are essential for environment-aware communication and sensing, providing location-specific wireless channel information. Existing RM construction methods often rely on precise environmental data and base station (BS) locations, which are not always available in dynamic or privacy-sensitive environments. While sparse measurement techniques reduce data collection, the impact of noise in sparse data on RM accuracy is not well understood. This paper addresses these challenges by formulating RM construction as a Bayesian inverse problem under coarse environmental knowledge and noisy sparse measurements. Although maximum a posteriori (MAP) filtering offers an optimal solution, it requires a precise prior distribution of the RM, which is typically unavailable. To solve this, we propose RadioDiff-Inverse, a diffusion-enhanced Bayesian inverse estimation framework that uses an unconditional generative diffusion model to learn the RM prior. This approach not only reconstructs the spatial distribution of wireless channel features but also enables environmental structure perception, such as building outlines, and location of BS just relay on pathloss, through integrated sensing and communication (ISAC). Remarkably, RadioDiff-Inverse is training-free, leveraging a pre-trained model from Imagenet without task-specific fine-tuning, which significantly reduces the training cost of using generative large model in wireless networks. Experimental results demonstrate that RadioDiff-Inverse achieves state-of-the-art performance in accuracy of RM construction and environmental reconstruction, and robustness against noisy sparse sampling.