They've got nothing to make a fuss about (sometimes): so, if you have a one megapixel image that was generated from one million training images, then each training image represents one millionth of the result. You've had nothing stolen from you, you're just anally annihilated.
However, if the AI pulls out the "essence" of Mickey Mouse, and makes a picture of what is clearly Mickey Mouse, then Disney has the right to sue, as they already do with all creators of fan art.
Really, the biggest thing with AI art is the legal status. In the US, the courts have ruled that AI art is fundamentally in the public domain, as AI isn't a creator, and the person pressing Enter isn't either.