Generally, whenever a company buys a photo, there's a release form where the claimed-author of the photo has to state that they own the rights to the photo. So, the infringement is on the part of the seller, and you have a high barrier to sue Adobe for that.
No, you don’t, Adobe just has a low barrier to suck the source of the image into the case as an additio al defendano and a potential additional de¹1¹fense against any claim of willful infringement.
OTOH, Adobe would like potential plaintiffs to think that it works the way you describe.
Exactly. Companies like Getty, Disney and Shutterstock are never tired of collecting money and the easiest target for this is Stable Diffusion, which is already commercializing the model with DreamStudio which includes Getty's images without their permission.
O̶p̶e̶n̶AI.com avoided this by partnering with shutterstock to get this permission first before training on their images for DALL-E 2. If O̶p̶e̶n̶AI.com was able to do that, then SD has no reason other than taking images without attribution or credit and using them commercially. (Which they have been caught many times)
Do they own the right to train-a-model? It's not clear at all. A lot of great photographers don't want their unique style to be multiplied ad infinitum. Copyright is to "copy, distribute, adapt, display, and perform a creative work", and this is not an adaptation
which is fine, if it's theirs they're free to do what they want with it
however I didn't give Microsoft permission to sell people code derived from my works without attribution
You can’t escape it, we may as well all benefit instead of this silly crusade making only 4 companies max benefiting, forever.
That being said, nothing is stopping Getty images, for example, from releasing their own image generator, trained from images they old copyright to.
Or creative common work, etc.