Teaching Diffusion to Understand Wireless Physics: Helmholtz-Guided Signal Generation

Generative models have recently demonstrated strong capabilities in learning complex data distributions and synthesizing signals. However, for wireless signals with real electromagnetic propagation characteristics, purely data-driven approaches can learn statistical patterns from observations but often struggle to capture the underlying propagation structures behind signal variations. Meanwhile, physics-based methods provide propagation-consistent signal modeling but typically require accurate scene information, limiting their applicability in practical wireless environments. Therefore, how to incorporate propagation principles into generative models without scene priors and enable signal generation with both statistical and propagation characteristics remains a key challenge. In this work, we propose Helm-Diffusion, a novel diffusion process guided by the Helmholtz equation that incorporates signal propagation principles into the generation trajectory. Helm-Diffusion exploits the propagation consistency implied by the Helmholtz equation to construct approximate representations of propagation structures from finite time frequency observations, and further derives static consistency for characterizing shared cross-frequency propagation structures and dynamic consistency for describing the evolution patterns of different frequency responses under changing propagation environments. Based on these propagation representations, Helm-Diffusion reformulates the stochastic generation process of conventional DDPMs by embedding propagation-structure degradation and recovery mechanisms into the progressive diffusion trajectory. This enables the generation process to incorporate propagation structure information while learning the statistical characteristics of wireless signals, achieving a synergistic integration of physics guidance and data-driven generation. Experiments on multiple wireless sensing and communication datasets demonstrate that Helm-Diffusion effectively improves generation quality over existing generative approaches while enhancing the consistency between generated signals and propagation characteristics, highlighting the effectiveness of physical laws as structured priors for generative models.