PC-DDPM: a physics-constrained denoising diffusion probabilistic model for ultrasonic defect response synthesis

Ultrasonic non-destructive testing (UT) is a fundamental quality-control tool in critical industries such as aerospace and petrochemicals, yet practical defect data suffer from limited sample sizes, class imbalance, and high annotation costs, hindering deep-learning-based intelligent detection. This paper proposes a Physics-Constrained Denoising Diffusion Probabilistic Model (PC-DDPM) for high-fidelity ultrasonic defect-signal synthesis, improving generation quality through three aspects. First, a physics-parameter conditional injection module based on cross-attention incorporates amplitude, frequency, and attenuation coefficient into the diffusion process. Second, a multi-dimensional physics-guided loss combining energy attenuation, frequency rationality, and time–frequency consistency terms is constructed; these terms are empirical regularisations derived from established ultrasonic-propagation relationships rather than PDE residuals, so the framework is physics-guided rather than PDE-based. Third, an adaptive denoising scheduling strategy dynamically adjusts diffusion step sizes according to signal complexity, balancing generation quality and computational efficiency. Experiments show that PC-DDPM reduces time-domain MSE by 63.7% and achieves a spectral similarity of 0.957 and a time–frequency correlation of 0.943 compared with baselines. Augmenting training data with generated signals raises four-class defect-classification accuracy from 82.8% to 95.0% (averaged over five independent runs), validating practical effectiveness in real inspection scenarios.