True, Njorl, diamonds are grown in factories and dead people are made into jewelry, all you need is some carbon and just apply a LOT of pressure to that, over weeks (or months) this diamond will grow.
The major problems with these diamonds were that they had impurities, like oxygen and nitrogen, changing the color of the stone. I think they have mainly overcome this problem now and they are coming to the point that these synthetic diamonds are almost indistinguisable from natural diamonds. The only way to tell at this point is to irradiate the stone, synthetic and natural diamonds react differently to this.
To reply about your question about industrial use: synthetic diamond is not the ideal all-purpose hard material. When heated up by friction in the presence of air, the diamond tends to decompose into carbon dioxide. And hot diamond dissolves in iron, so it can't be used to cut steel. There is actually a material better fit for this purpose Cubic boron nitride (cBN), first made in 1956, half as hard as diamond but more stable under those extreme circomstances.
Here an article about the dead-person-made-into-a-diamond: