The author is the one that records it, not the tool used to create it.

Nothing AI created can have copyright under current law.

In the US, indeed. But in the UK the runner of AI can hold a copyright. Which I think is stupid but that's hardly the first dumb copyright thing.

For something like img2img with Stable Diffusion, if the starting image is copyrighted by someone else I'd expect that the output image is a derivative work of the starting image.

The question is about new copyright in both cases, not subsisting copyright. You hold the copyright to the elements originating with you in a derivative work.