Question regarding neural networks for denoising

I'm very to new to machine learning in general and am reading Marsland's textbook. He briefly mentions that neural networks can be used for denoising an image. From my understanding, the network is trained on a generally high-quality version of the image. If this is the case, then what is the purpose of a denoiser if the high-quality image is already available? Is the network capable of generalizing to slightly different pictures? I'm sorry if I am completely wrong in my assumptions or if this question is just silly.