A diamond will burn

Diamond is carbon. Heated in oxygen to roughly 700 to 900 °C, it oxidises and is gone. It does not melt in any ordinary fire.

In 1772 Lavoisier and his colleagues focused the Sun through large lenses onto a diamond in a sealed vessel and showed that the diamond lost mass and that the gas in the vessel changed as it does in combustion. Diamond is carbon, arranged one way. Graphite is carbon arranged another way. Either can be oxidised to carbon dioxide if you supply heat and oxygen.

In air the temperature has to be high and held there. A house fire can damage or destroy a stone; a brief match cannot. Without oxygen, diamond does not burn, and the conversion toward graphite at room pressure is immeasurably slow at any temperature a jeweller's torch reaches in open air. 'Forever' was always a sales word.