Pulse width parameter in VI Characteristic curve of Diode
The pulse width and duty cycle is an explanation of how they measure the instantaneous forward voltage parameter. This is how you would set up the test equipment to verify that the diodes meet specifications. 

You can't measure the voltage without putting current through the diode. You can't put current through the diode without changing the die temperature, so the forward voltage for longer pulse widths and larger duty cycles would appear to be lower or higher because the die heats during the pulse or over a number of pulses. 

For low currents the forward voltage decreases with temperature as you might expect for a diode, but for extremely high currents the Vf temperature coefficent actually goes through a null at something like 10-20A and becomes positive because the non-ideal resistive term dominates, and it has a positive tempco.  

The Tj, although specified as 25°C cannot remain constant.