Once a diamond melts and loses its crystal structure, it's just ordinary old carbon. Of course, liquid carbon doesn't sound nearly as cool as liquid diamond.
Yeah, that's what I was thinking as well. The only thing that differentiates diamond from other forms of carbon is the crystal structure. Diamond has a wonderfully symmetrical interlocking lattice, which is why it's so strong. Pencil lead is composed of exactly the same thing - carbon, but the atoms in graphite are arranged in sheets which easily separate from each other, which is why pencils write so well.
If you've got a liquid, obviously you can't have a crystal structure. But still, it sounds cool