Seismic data denoising via supervised deep learning is effective and popular but requires noise-free labels, which are rarely available. Blind-spot networks circumvent this requirement by training directly on noisy data and have been demonstrated to be a powerful suppressor of random noise. In this work, we expand the methodology of blind-spot networks to create a blind-trace network that successfully removes trace-wise coherent noise. An extensive synthetic analysis illustrates the denoising procedure’s robustness to varying noise levels and varying numbers of noisy traces within shot gathers. It is demonstrated that the network can accurately learn to suppress the noise when up to 60% of the original traces are noisy. Furthermore, our procedure is implemented on the Stratton 3D field data set and demonstrates the restoration of the previously corrupted direct arrivals. In addition to trace-wise noise suppression, we adapt the blind-spot networks to the successful suppression of colored Gaussian noise, which exhibits varying coherent properties in time and spatial axes. Our adaptation of the blind-spot networks paves the way for its use in other applications, such as the suppression of coherent noise arising from wellsite activity, passing vessels, or nearby industrial activity.