I've noticed that the diamonds we've been introduced to have different personalities. Yellow diamond is the strict, impatient type, while blue diamond is more of the gloomy, somber type. Could it possibly be that the diamonds are the fragments of a more powerful gem, broken into 4 parts that each represent one of its emotions?
I know there is also a pink diamond, which could represent happiness or enthusiasm. The fourth gem's information is a bit more sketchy; it may not even exist. It's possible that the fourth gem is a red diamond, representing anger, malice or maybe greed. If this is true, the four diamonds could be fragments of a larger diamond, more powerful than them all combined. Of course, I shouldn't say that, because it IS all of the combined.