All of these are held together by very, very strong chemical covalent bonds and that means that you need to heat up elemental carbon a huge amount before you can actually start to separate those atoms. In fact, once you heat it up to about 3,600 degrees C, you finally get to pull those atoms apart and it turns into a gas: it sublimes; so it normally goes from a solid to a gas. If you want it to be a liquid, you have to put it under incredible pressure while you're actually heating it up that much. So, it's only under very, very extreme circumstances that you can force carbon to be a liquid.
Given the mantle pressures, it becomes plausible.