Textbooks and the online reference differ about this and there are more than two answers.
Diamond (carbon) does not melt at 1 atm. It sublimes to vapor.
Using carbon's theoretical phase diagram below (from Wikimedia), "liquid diamond" could be achieved at about 10 GPa (99 thousand atmospheres) and 5000 K (4700 °C).
In fact, heating up diamonds at 1 atm turns them into graphite first. Only further heating would cause sublimation, as expected by observing the phase diagram. Here's a video: