What is the origin of diamonds?

From Wikipedia:

"Diamonds are thought to have been first recognized and mined in India, where significant alluvial deposits of the stone could be found many centuries ago along the rivers Penner, Krishna and Godavari. Diamonds have been known in India for at least 3,000 years but most likely 6,000 years."

(An alluvial deposit is formed when water flows over the volcanic pipe that erupts diamonds to the surface of the earth and tumbles the stones into the riverbed.)