Yes, the De Beers Group of Companies is a diamond cartel that had complete control of the diamond market for most of the 20th century. They still control a sizable portion of the market and their effort at marketing (particularly with the slogan "A Diamond is Forever") has done much to inflate the market for diamonds in our society.
The intrinsic value of diamonds is much lower than the market prices currently reflect, but with the caveat that there is a rarity factor which does drive up the price of larger diamonds.
The larger the diamond, the more likely it is to have flaws, so when it comes to diamonds that are 5 carats or greater, you are not as likely to see a new supply of diamonds disrupt the prices of those larger stones.
Some other ways that high end jewelers and suppliers are differentiating themselves is by patenting a specific cut that they design. This is another barrier to entry that works to create some artificial price inflation. One common example is the Lucida cut sometimes referred to as the Tiffany cut.
Diamonds can also be manufactured. The same carbon structure can be grown in a lab. These stones have the same carbon structure as natural diamonds but without the flaws and visible impurities. Most manufactured diamonds are used industrially, but processes have improved sufficiently to allow for gemstone quality synthetic diamonds. They sell at a decent discount, so that might be an option to consider if you want a substitute. In the years to come, you can expect prices for synthetic diamonds to continue to decrease which will probably put some further downward pressure on jewelers' prices.