Diode parallel to resistor on H-Bridge MOSFETs gates
The upper MOSFETS are P-channel, and the lower ones are N channel.

MOSFETs need the gate voltage to be roughly equal to the source voltage to turn them off.  For the N-channel lower MOSFETs that's ground.  For the P-channel upper MOSFETs that's "+5 to +15V".

P-channel MOSFETs are notoriously slow to turn off (slower than N-channel).  Adding the diode allows the voltage at the gate to rise to the "+5 to +15V" level much faster at the cost of increased current.

The resistors slow down the turn-on of the P-channel MOSFETs giving the N-channel a chance to turn off first.

It's all about reducing the chances of shoot-through and engineering a dead zone in the switching - make sure the P-channel turns off before the N-channel switches on, and vice versa.

If you were to put resistors on the N-channel MOSFET gates as well it would negate much of that effect by slowing down the switching of the N-channel MOSFETs.