[seanhunter]

Copyright defines the use of a work. If training a model is not allowed under copyright law, it doesn't matter whether or not a work produced by that model is derivative or not (or even if the model produces no works at all)- the training itself is a copyright violation.

In the case of the US fair use doctrine, there is a four factor test which applies[1] one leg of which is the effect of the use on the potential market for the original work. In the example you gave "studying the old masters", it is trivially true that studying an old master has no effect on the future market for those paintings. However I believe copyright holders may well have a stronger argument about the possibly impact of generative AI on the market for their future work because of the ability of people to generate pastiches of their work. Even if those are not deemed to be derivative (which they may or may not be), the use of the original in training could be deemed not to be fair use because it affected the market for the original.

It's nowhere near as cut and dried as people on either side of this debate seem to be making out.

[1] https://fairuse.stanford.edu/overview/fair-use/four-factors/