I need help understanding constant voltage model for diode

So I'm confused about the constant voltage model (which assumes diode has .7 volt drop).

In the pic below, I'm confused about the third case. What if the voltage source has voltage less than .7 V but the diode is in forward bias? Does that mean it's open circuit and hence the voltage drop across the diode will equal that of the voltage source? (In the last two cases---in the circuits to the right--I just made up numbers to illustrate the concept)