The model can generate original images, yes, and those images might be fair use. But it can also generate near verbatim copies of the source works or substantial parts thereof, so the model itself is not fair use, it's a wholly derivative work.

For example, if a publish a music remix tool with a massive database of existing music, creators might use to create collages that are original and fall under fair use. But the tool itself is not and requires permission from the rights owners.