I'm not entirely up to speed on what the laws are like internationally, but where I'm at there's the concept of "portrait rights" which basically amounts to you having rights to a photo made of you. The photographer gets the copyright, but he's not allowed to distribute the photo without your say so since you own the portrait rights. There's a couple of fairly sane exceptions such as crowd photos, you need to be the actual subject of a work for portrait rights to apply.

It'd be a fairly boring application of these laws to say that you have portrait rights to any deepfake of you.

Furthermore I think refering to a deepfake as an image in your likeness is selling it short. A deepfake is more akin to a mashup of a lot of photos of you. A deepfake doesn't just look like a person, it's made from photos of that person.

Not sure how this line of thinking would apply to other countries, but it seems like a viable framework for regulating the whole thing to me.

I think it's odd, I believe copyrights are owned by the photographer. I think they should have specific claim to the copyright, but at any time should be required to take down and destroy pictures when a person in said picture decides they don't want to be in it. Though w/ digital-ness that may be nigh impossible, maybe they could make a DRM image that if you delete the master all images across the web cease to work. That would definitely be an interesting technology.