The damages arise from the very process of stealing material for training. The justification "yes but my training didn't cause me to directly copy the works" is faulty.

I won't rehash the many arguments as to why the output is also a violation, but my point was more the absurd view that stealing and using all the data in the world isn't a problem because the output is a lossy encoding (but the explicit training objective is to reproduce the training text / image).