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.
In that case, Yellow Diamond could embody anger and greed, while White Diamond could be perhaps apathy or timidness. Red Diamond could be the combined four, as it is one of the rarest diamonds found to date.
What if White diamond is a fusion. White is seen as neutral and pure, which seems like the personality you would get if you got all the personalities of the diamonds and mixed them. It would also explain why she's seen as the matriarch in the logo. It makes sense now that she hasn't shown up yet.