"The diode probably protects against reverse polarity supply connection."Perhaps so, but the back EMF from the stepper coils will hammer the darlingtons without that escape path!
Isn't that's why you put a snubber diode, and perhaps a parallel ceramic capacitor, across the motor coil?
Ah yes, that diode is rather suspicious now... Note that motors aren't pure inductance, each half of each winding is coupled to the other half, which may in practice limit the inductive spikes from a unipolar motor in certain modes.And there is the issue of step speed - diodes across the windings slow the motor's response down (a diode and zener diode pair per winding can be used to tame the spike and speed up switch-off)
I've gotten this code to work at 2000 steps/sec using 12v.http://arduino.cc/forum/index.php/topic,89159.0.html