Boost Converter - How the diode keeps conducting?
Your question asks about what happens when there's 0 V across the diode.

There are only two states for the diode voltage that persist long enough to matter. One is the switch open, diode conducting state, with current flowing from the inductor to the load, and charging the output capacitor. The diode voltage is 
a small forward drop, usually less than 1 V. The other is the switch closed, diode blocking state with Vo across it, while the output capacitor supplies the load current, and the inductor recharges from the input. 

The diode voltage does pass through 0 V twice per cycle, once at the switch off transition, once at the switch on transition. At that instant, the diode is not conducting, just as it's not conducting for the entire blocking phase.