Physics-constrained diffusion-based data augmentation for active sonar under low-SNR sea conditions

The limited availability of real sea-trial target echoes restricts the training of data-driven active sonar detection models. Simulated echoes can increase the sample size, but their distributions often differ from those of real ocean environments. To address this problem, this paper proposes a physics-constrained two-stage unconditional diffusion model for data augmentation of active sonar linear frequency modulation (LFM) echo spectrograms. In the first stage, a denoising diffusion probabilistic model (DDPM) is pre-trained with synthetic LFM echo spectrograms to learn the basic time–frequency structure of target echoes. In the second stage, a small number of real sea-trial samples are used for structure-preserving fine-tuning, where the pre-trained model serves as a frozen teacher and a structure-preserving loss constrains structural drift while adapting to realistic reverberation and background-noise statistics. A spatial-frequency selective convolution module and an embedded spectral energy limiter are introduced to improve spectral-structure modeling and suppress unstructured background responses. Experiments show that the proposed method achieves better distributional similarity and physical consistency than representative generative baselines. Downstream binary detection experiments further demonstrate that the generated samples provide effective data augmentation under low-SNR and cross-area background-noise conditions, improving the robustness of active sonar detection in complex ocean environments.