"Deep Fakes" in general seem to be already covered by existing libel laws, though that has some problems. Libel is generally a civil matter, and is extremely difficult to prosecute.

There is precedent, even in the US, for criminal libel laws[0]. Perhaps following that path (combined with continued work on detection and defeat of the technology) would be preferable. Since libel and defamation are well-defined and have a long history of jurisprudence, many of the constitutional and legal issues which would have to be answered in opening a new avenue of speech restriction could be contained within the existing contexts.

I'd even think leaving it in the civil arena would make sense until it became a problem worthy of criminalization. Legislating a matter before it arises is almost never a good idea, from either a prudential or principled standpoint.

[0] https://www.washingtonpost.com/news/volokh-conspiracy/wp/201...