Twitter will remove nonconsensual nude images within hours as long as that media is reported for having violated someone’s copyright. If the same content is reported just as nonconsensual intimate media, Twitter will not remove it within weeks, and might never remove it at all, according to a pre-print study from researchers at the University of Michigan.
This isn’t true or how it works, but there is a law being proposed that would sorta make it so: https://arstechnica.com/information-technology/2024/08/senates-no-fakes-act-hopes-to-make-unauthorized-digital-replicas-illegal/
(In the US), your likeness is protected under state laws and due to case law, rather than federal laws, and I don’t know of any such law that imposes a responsibility upon sites like Twitter to take down violations upon your report in the same way that the DMCA does. Rather, they allow you to sue the entity who used your likeness for damages in civil court. That isn’t very useful to Jane when her ex-boyfriend uploads revenge porn of her or to Kate when a random Twitter account deepfakes her face onto a nude.
However, if a picture you have copyright to (like a selfie) is used as an input into an AI, arguably you do have partial copyright to it, as the AI elements are not copyrighted and it could not have been created without your input. As such, I think it would be reasonable to issue a DMCA takedown request if someone posted a nonconsensual deepfake of you, on the grounds that you have a good faith belief that you do have copyright to it. However, if you didn’t take the picture used as an input yourself, you don’t have copyright to it and therefore don’t have partial copyright to the output, either. If it’s a deepfake face swap, then whoever owns copyright of the original scene image/video would also have partial copyright, and they could also issue a DMCA takedown request.