Seismic waves contain information about the earthquake source, the geologic structure they traverse, and many forms of noise. Separating the noise from the earthquake signal is a critical first step in seismic waveform analysis. This is, however, a difficult task because optimal parameters for filtering noise typically vary with time and, if chosen inappropriately, they may strongly alter the original seismic waveform. Diffusion models based on Deep Learning (DL) have demonstrated remarkable capabilities in the restoration of images and audio signals. However, those models assume a Gaussian distribution of noise, which is not the case for typical seismic noise. Diffusion models trained on Gaussian noise do not perform well in seismic applications; therefore, we introduce a "cold" variant of diffusion models in which both clean and noisy seismic traces are restored. Here, we describe the first Cold Diffusion Model for Seismic Denoising (CDiffSD), including key design aspects, model architecture, and noise handling. We demonstrate that CDiffSD provides a new standard in performance, outperforming existing methods. Our model provides a significant advance for seismic data denoising and establishes a new state-of-the-art in the field.