Purpose of anti-parallel diodes in isolated gate driving circuit?
But what is the purpose of the anti-parallel switching diodes, D1-D2? They appear to be in a clipping/limiting configuration, but I cannot figure out why they're needed. 


Without further information regarding your schematic, the diodes (D1, D2) aren't needed for the circuit to operate. 

When +15 volt input pulse is applied, the MOSFET (M1) will turn on.  When +15 pulse is removed (input volts = 0), the M1 remains on (at least as long as the gate charge remains). When -15 is applied, M1 will turn off and remain off.  

It is D3 (zener) that is used to block discharge of the gate, so that M1 remains on even when input pulse goes from +15 to zero volts.    





Green =  Input pulse V1
Red   =  Voltage at gate of M1
Yellow=  current in R1 (10 ohm resistor), effectively gate current  

The diodes (D1 and D2) just cause a diode voltage drop on the input pulse. The diodes would also provide some (minor) damping (just like R1 would) if inductance was in the gate circuit and caused ringing.   

EDIT :   The following is without the anti-parallel diodes (replaced with a wire).