Update: I watched the BBC special on synthetic diamonds (https://www.youtube.com/watch?v=5d2WebdMpBQ) and De Beers shows you can tell the difference between synthetic and real diamonds by their reaction to UV radiation. I am still interested in how I can make a DIY diamond if anyone has details on that. And to make this more on topic, how best I can simulate the Earth's formation of diamond? Why is the Earth's formation of diamond different from these HPHT and CVD diamonds?

The big question is how do you make gemstone quality diamonds. Chemical vapour deposition seems like the most successful method. There are other methods, but it's pretty easy to distinguish them from natural diamonds (example). It is still quite hard to do it: it's not something anyone can just do in their backyard. With technology it becomes easier though. Here comes the question of regulation. Gemesis, one of the companies that makes them, engraves a serial number using laser on each synthetic gem-quality diamond they make. But what about some evil diamond makers who want to simulate natural stones? As with any other synthetic material, there are imperfections that are different from imperfections found in natural stones. Moreover, each mine or region where diamonds come from has a different fingerprint (they use that to trace blood diamonds). There are methods to analyse the diamonds to detect this. UV and IR spectroscopy, laser ablation, isotope analysis, cathodoluminescence and others. Some are easier and cheaper than others.

So you can't just make up impurities to say "look it's natural", they have to be consistent with a specific diamond source you're trying to imitate. And that's - not very easy. Likely impossible with today's technology.