That's what Diamond Foundry, the SF startup, is doing. They have a good story: "We produce gem quality diamonds above the ground in America — in harmony with nature and humanity. A carefully chosen earth diamond is at the origin of each of our diamonds. In the perfectly nurturing environment inside our foundry, diamond crystals want to continue to grow."
The CEO was the founder of Nanosolar, which printed solar cells and went bust because, although the process worked, it wasn't cheaper. The investors in Diamond Foundry are the usual suspects - Zynga's founder, Sun Microsystem's founder, Facebook's co-founder, a former eBay CEO, etc. They even have an actor, for coolness. An endorsement by Leonardo DiCaprio: “I’m proud to invest in Diamond Foundry Inc.– reducing the human and environmental toll of the diamond industry by sustainably cultivating diamonds without the destructive use of mining.” It's a classic startup story.
They claim to be "0.001% Rare"; this reflects their market share, like a microbrewery. Their big problem seems to be distribution. Only five small jewelers handle their product. De Beers punishes jewelers who do things they don't like by excluding them from "sights" where jewelers can buy diamonds at wholesale prices. This makes it hard for competitors to get access to retail outlets.