There's actually been some litigation around this topic recently. The general consensus seems to be that authorship gets assigned to closest version of the person who initiated the creation process of the resulting artwork. So, in this case, I believe it would be the person that selected and uploaded the photo to the service would have authorship--the actual process is considered to be more of a blackbox tool being used by that person. A (way more) sophisticated digital paintbrush, if you will.
Wouldn't this be similar to using Photoshop or any other image manipulation tool? Adobe does not get ownership of output of their software. Why would we think some random website offering image manipulation would be different? As you say, the software is just a tool in the image creation process.
what gets really messy is the training data. Renaissance paintings are (hopefully?) all public domain, but what would be the case if I used living artists' work, or the collection of disney cartoons?
The pictures themselves are probably public domain, the photography of the picture however might be protected (photographer picked angle, lense, lightning, ...)
I'm not sure about links directly to court cases, but here's a couple different general-consumption articles from the last few years that address this sort of thing. I'm hopeful I didn't convey that the consensus on the subject is particularly solid...
Thanks for the links. I know little on the topic. It may be a while before a litigious content owner identifies their work as having contributed to another generated one. I have yet to see in-your-face examples being monetized.
From a technical standpoint using copyrighted text to train a text translator is similar to using copyrighted movies to train a movie generator. Which of these are acceptable?
https://imgur.com/a/hkG0rJg
https://imgur.com/a/YZ3oWUm