Synthetic seismic signal generation plays a critical role in various geophysical applications, including imaging, seismic exploration, and earthquake simulation. Traditional methods of generating seismic signals often rely on empirical models or numerical simulations. One issue with such methods is their computational cost when it comes to generating high-frequency signals, thus limiting their ability to capture the complex nature of real seismic records. In recent years, deep learning techniques have emerged as powerful tools to generate time series, images, videos, text and to solve partial differential equations. In this study, we propose a novel deep learning diffusion model enabling the generation of broad-band (0-30 Hz) seismic signals, both unconditionally and conditionally by conditioning the generation with a low-frequency simulated signal. By adopting a diffusion-based approach, the model captures the temporal and frequency dependencies inherent to seismic data. The generative architecture employs a UNet, a model originally developed for image segmentation tasks but later proven highly effective in diffusion-based generation. We adapted this UNet architecture by incorporating 1D remodeled versions of BigGANDeepUp and BigGANDeepDown blocks, along with a cross-attention mechanism, to enhance its performance for our specific application. Additionally, we used an xGBoost model to predict the amplitude of the high frequency signal using the low frequency one. The results show that our generative diffusion-based deep learning model enables the generation of broad-band high-fidelity seismic signals. The generated synthetic signals exhibit realistic seismic characteristics in both time and frequency, making them suitable for applications such as seismic data augmentation, improvement of synthetic earthquake modelling. When conditioning with the low-frequency numerical simulation, our model can effectively achieve a one-to-many broad-band generation, which is particularly useful in the framework of probabilistic seismic hazard assessment.