EMDiC: Physics-Informed Conditional Diffusion Denoising for Frequency-Domain Electromagnetic Signals

Frequency-domain electromagnetic (FDEM) measurements for shallow subsurface exploration are frequently corrupted by noise, which masks weak secondary-field responses and degrades interpretation. We propose an electromagnetic diffusion CNN (EMDiC) for 1D multi-frequency FDEM denoising, where denoising is formulated as conditional diffusion-based generation. EMDiC combines an analytic frequency–spatial encoder, a Feature-wise Linear Modulation (FiLM)-conditioned convolutional hourglass backbone, and a physics-informed composite loss built on velocity loss to improve waveform reconstruction under severe noise. A reproducible synthetic dataset is constructed through layered-earth forward modeling with concentric Transmitter–Receiver (TX–RX) geometry, multiple target categories, and mixed noise waveforms. On synthetic benchmarks covering multiple noise levels and material types, EMDiC achieves the best overall performance in Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), and Normalized cross-correlation (NCC) among 1D U-Net, diffusion-based variants, and representative neural baselines, with the clearest gains under medium-to-strong noise and for targets with pronounced induction responses. Ablation experiments verify the complementary contributions of electromagnetic positional encoding (EMPE), FiLM conditioning, and the composite loss. Field data validation with a self-developed GEM-3 system further shows that EMDiC improves cross-frequency coherence and suppresses oscillations while preserving the main response characteristics.