Purpose of diodes on ADC inputs in DRV8305 example circuit?
They are protection diodes (aka clamping diodes) which are there to ensure that if the voltage starts to go above a certain amount (in this case the Vcc supply rail) that they will start conducting and try to prevent it rising any further.

Motors are noisy, and during switching you can get spikes at the centre of the h-bridges that are much higher than the motor supply rail (they can be on the order of tens or even hundreds of volts if not careful). This means that the spikes would cause the voltage at the sense pins to rise up much further than they are rated for.

By adding the diode, if the voltage rises up above Vcc, the diode conducts and increases the voltage drop across the upper resistor in the potential divider to clamp the voltage to no more than Vcc plus the diodes forward voltage. As such a Schottky type diode is used, as indicated by the box-like ends of the cathode bar in the symbol, as they have a much lower forward voltage than a standard PN diode which in turn reduces the amount above Vcc which the sense pin can reach.