The matter is that semiconductors and ohmic contacts have resistance and too create voltage drop which is added to 0,7 volts of voltage drop at pn junction. As far as I know, HV diodes has more high resistance of semiconductor that another diodes. Therefore, the voltage drop on the diode you are interested in is 1.1 volts at a current of 1 amp, but the voltage drop at pn junction is 0.7 volts approximately, and everything else is ohmic losses. At low direct currents this voltage will not exceed 0.7 volts and can be measured with a DMM.
There are diodes that can not afford a DMM

This is HV diode array. Now I uses amperemeter and voltmeter for testing. Direct current 8 mA, drop voltage 18,6 V

These are diodes that cannot be measured with a conventional DMM. In datasheet says that maximum drop voltage equal 25 V at 10 mA current, therefore they passed the test:)