I'm not sure I'm understanding your question, so if my answer is not what you were looking for, sorry.
The way a diode works is like this: You apply a forward voltage across it. Starting from zero, no current flows through the diode. As you ramp up the voltage, a very small current (microamps) starts to flow. When you reach a certain voltage, which is around 3 V for an XM-L LED for example, all of a sudden the diode starts to conduct lots of current (amps), assuming the power source is capable of producing unlimited current. The diode behaves more or less like a piece of wire once you reach that voltage. If you increase the voltage too much, e.g. 3.5 or 4.0 V, without any limiting devices like a series resistor, the current through the diode flies through the roof and if the diode isn't capable of dissipating the generated heat, poof.
If you do use a series resistor, you can flatten out the curve, so to speak. As you ramp the voltage beyond 3 V, the diode behaves more or less like a piece of wire, but the resistor prevents the current from flying through the roof.
So what this means is that you don't apply a certain voltage across the diode and then independently push a certain amount of current through it. The voltage across the diode determines the amount of current through it.
See the first graph on this page: http://www.kpsec.freeuk.com/components/diode.htm
That graph is for a general purpose diode. As I mentioned, for an XM-L LED, the "knee" is around 3 V instead of 0.7 V.
So when you ask if there's a reference voltage, I'm not quite sure what you mean, but given a specified current through the diode, you can look at the diode's data sheet to find out what the voltage must be.
Aside: one of the reasons that the XM-L is such a good LED, compared to older ones, is that its forward voltage is lower. What that means is that it takes less voltage before the LED starts to conduct current, and therefore it operates at a lower voltage at a given current, and that means lower power draw at a given current.