There have not been enough court cases to tease out the detais. Broadly speaking, it will hinge on a very subjective interpretation of "transformative." If it's transformative enough, the person who ran the machine can claim copyright (assuming there's not some entanglement built into the software itself attempting to claim copyright for all products it generates), not unlike how a person who operates the camera claims copyright on the photograph.
(To my eye, it's extremely transformative because there's no single, or even three or five, pieces of artwork you could point at to see where the AI derived the data from, but IANAL).
