The diamond is the lasting symbol of purity and incorruptibility, due to its form in nature as a stone that cuts all but cannot be cut itself.
This interpretation, however, most likely came as a result of the "drawn" diamond, which represents two triangles joined at the base. The two triangles represent Man (downright) and the Universe (upright), or the Microcosm and the Macrocosm, emanating from God. The symbol reminds us that Man is within the Universe and the Universe is within Man; the goal is to unite the two such that they become inexorably linked -- one whole, which is to say, God.
Adopted by mystics and alchemists as the symbol of achievement -- or perfection -- it came to represent what was believed to be the lifestyle necessary to achieve such a level of Unity: One that was both pure and uncorrupt. From there arose the notion that a stone with similar qualities must be the very physical embodiment of the drawn Diamond.
The symbol reminds us that we must travel through the Tree of Life to become reunited with the Kether (the crown or God).