What you are describing is the essence of what copyright is intended to do. It allows artists to retain some ownership and control of their work, while at the same time allowing other artists and interested parties to observe and learn from it. However, AI is not "other artists", there is no human mind performing a creative act in the process. It's a reproducible algorithm. If you saved the state I'd an image generator, it should give you the same output for a given input*. We just give extra weight to the human factor. Eventually the legal system will weigh in on it, and the other side will have some clever argument of their own, but it's the humanity that matters**.
*I also wouldn't be surprised if someone thought they would be "clever" and toss in some randomness to make this seemingly impossible, but it's still just a matter of replicating ALL inputs precisely.
**I guess Data really is Starfleet property.