In this paper, we propose a novel physics-informed generative learning approach, named RadioDiff-$k^2$, for accurate and efficient multipath-aware radio map (RM) construction. As future wireless communication evolves towards environment-aware paradigms, the accurate construction of RMs becomes crucial yet highly challenging. Conventional electromagnetic (EM)-based methods, such as full-wave solvers and ray-tracing approaches, exhibit substantial computational overhead and limited adaptability to dynamic scenarios. Although existing neural network (NN) approaches have efficient inferencing speed, they lack sufficient consideration of the underlying physics of EM wave propagation, limiting their effectiveness in accurately modeling critical EM singularities induced by complex multipath environments. To address these fundamental limitations, we propose a novel physics-inspired RM construction method guided explicitly by the Helmholtz equation, which inherently governs EM wave propagation. Specifically, based on the analysis of partial differential equations (PDEs), we theoretically establish a direct correspondence between EM singularities, which correspond to the critical spatial features influencing wireless propagation, and regions defined by negative wave numbers in the Helmholtz equation. We then design an innovative dual diffusion model (DM)-based large artificial intelligence framework comprising one DM dedicated to accurately inferring EM singularities and another DM responsible for reconstructing the complete RM using these singularities along with environmental contextual information. Experimental results demonstrate that the proposed RadioDiff-$k^2$ framework achieves state-of-the-art (SOTA) performance in both image-level RM construction and localization tasks, while maintaining inference latency within a few hundred milliseconds.

翻译：本文提出了一种新颖的物理信息生成学习方法，名为RadioDiff-$k^2$，用于实现精确且高效的多径感知无线电地图构建。随着未来无线通信向环境感知范式演进，无线电地图的精确构建变得至关重要，同时也极具挑战性。传统的基于电磁学的方法，如全波求解器和射线追踪方法，存在显著的计算开销，且对动态场景的适应性有限。尽管现有的神经网络方法具有高效的推理速度，但它们对电磁波传播的底层物理原理考虑不足，限制了其在精确建模由复杂多径环境引发的关键电磁奇异性方面的有效性。为应对这些根本性局限，我们提出了一种新颖的、受物理启发的无线电地图构建方法，该方法明确地以描述电磁波传播本质的亥姆霍兹方程为指导。具体而言，基于对偏微分方程的分析，我们从理论上建立了电磁奇异性（对应于影响无线传播的关键空间特征）与亥姆霍兹方程中由负波数定义区域之间的直接对应关系。随后，我们设计了一个创新的基于双重扩散模型的大型人工智能框架，其中一个扩散模型专门用于精确推断电磁奇异性，另一个扩散模型则负责利用这些奇异性以及环境上下文信息来重建完整的无线电地图。实验结果表明，所提出的RadioDiff-$k^2$框架在图像级无线电地图构建和定位任务中均实现了最先进的性能，同时将推理延迟保持在数百毫秒以内。