I imagine an image generated using a prompt like "a chicken" would not be copyrightable. However, a prompt like "Asian girl with pink hair playing the piano with two brown pomeranian dog in her lap." would produce a copyrightable image.

The real question is, how long does the prompt need to be to satisfy the minimum human creativity requirement.

Presumably, the random noise used as input will be different. As for the minimum creativity necessary for copyright, the prompt should suffice.