RadioDiff-$k^2$: Helmholtz Equation Informed Generative Diffusion Model for Multi-Path Aware Radio Map Construction

TL;DR

This paper tackles multipath-aware radio map construction for environment-aware wireless networks by introducing RadioDiff-$k^2$, a physics-informed diffusion framework guided by the Helmholtz equation. It combines a Helmholtz-informed singularity map with a two-stage latent diffusion model (VAE+denoising U-Net) to first localize EM singularities (regions with $k^2<0$) and then reconstruct the full RM conditioned on environmental context and base station location. The approach yields state-of-the-art performance across static and dynamic propagation scenarios (SRM, DRM, MRM) with competitive latency, and it demonstrates strong downstream localization improvements. This physics-guided diffusion framework bridges physics-based EM propagation with data-driven generative modeling, enabling accurate, efficient, and robust RM construction for real-time 6G and beyond applications.

Abstract

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.

Figures (9)

• Figure 1: Illustration of the RM, where (a) is the RM only considering the dominating path, (b) is the RM considering the multi-path effect, and the propagating path is shown for a specific location.
• Figure 2: Illustration of RMs constructed by various NN-based baseline methods, where RadioDiff is the SOTA NN-based RM construction method. The results indicate that existing NN-based approaches exhibit limited capability in capturing fine-grained texture features of the RM, particularly those associated with abrupt spatial variations in wireless channel characteristics. This deficiency hinders the ability of these methods to reliably detect electromagnetic singularities, thereby limiting their effectiveness in downstream wireless network optimization tasks.
• Figure 3: Illustration of the different texture extraction methods.
• Figure 4: Illustration of the proposed two-stage diffusion framework. (a) Training: The $k^2$ map is derived from the Helmholtz equation and GT, and points with $k^2<0$ form the Map Outline, refer to the Helmholtz-informed singularity map, used to train a dedicated DM. (b) Inference: Without solving the Helmholtz equation, the first DM predicts the Map Outline, which, together with environmental information, guides a second DM to generate the RM.
• Figure 5: Illustration of the training details.