Is a diode's forward voltage stable enough to be used as a reference voltage?
Is a diode's forward voltage stable enough to be used as a reference
  voltage?


No, it will change with temperature: -



Picture taken from here

At 25 degC and a bias of 5.1 mA (for example) the voltage will typically (that's typical and not always) be about 627 mV. At 30 degC the voltage will have dropped to about 618 mV - that's a change of 1.4% for a minor difference in temperature. In voltage reference terms that's a stability of 2878 ppm/degC. Compare this to just fairly cheap voltage references having a drift of 50 ppm/degC. 


  Assuming a constant, preferably low current (1mA) is applied to a
  diode


If you have a constant current source then apply it to a resistor and you'll get pretty much stable results compared to the diode.