Logic gate using current source and diodes
There are 2 ways to understand this.


Replace Current Source with a "Voltage source with a resistor in series (+ve where current goes out)". Now you can imagine that there will be output only if both diodes are blocked, otherwise all current will be grounded.
A current is originating from source and it needs a path to ground. It always selects a low resistance path. If N terminal of diode is grounded (logic 0 attached), it is forward bias (ideally there is no +0.7V required). Current takes 0 resistance path irrespective of load and hence 0 output. If any voltage is attached at N terminal (logic 1), it will be reverse bias and so open circuit, current will go to output.


Other than that, practically speaking, HIGH logic state in practice never behaves as ground (0), although at times it may behave as 1.