That depends on the diamond.
Yes the diamond market does control how many white stones are on the market, mostly mid-grade stones. Keep in mind that many diamond mines are located in areas that are difficult to get to or in places of the world where wars are all too frequent.
But there are other diamonds, fancies, which are extremely valuable because of their rarity. Fancy diamonds come in many beautiful colors-yellow, orange, brown, purple, black, pink, blue, green and red. Those are not controlled because they are so rare and highly collectible. When the World Trade Center was destroyed on 9/11, a collection of orange diamonds was lost in the disaster.
Contemporary jewelry-grade diamonds, such as the ones you'd find in most commercial jewelry, are not rare. But diamonds that have no flaws and are of considerable size (over 10 carats) are so rare that few have ever seen such a stone, much less purchased one.
One reason diamonds appear to be more available and less rare is the explosion of lab-created stones on the jewelry markets. These non-natural stones are considered less valuable because of how they're made. It's difficult for the layperson to know if the stone in their jewelry is natural or lab-created. In some cases, jewelers have been known to replace good quality natural stones with lab-created ones.