An opamp operating in its linear region has effectively no voltage between the inverting and non inverting inputs (that is to say is has a VERY large open loop gain and that this condition is maintained by feedback).
In normal operation the current sense amplifier drives its feedback loop to maintain almost no voltage between its inputs, however in the event of an overload or startup excursion the two diodes clamp the voltage difference to avoid some of the weirdness that can happen with opamps if you force the inputs too far apart (In this opamps and comparators differ, comparators are designed to run with significant differential mode input, opamps not so much (There are other differences).
Regards, Dan.