How does the differential cap at the input to an ADC/amplifier help reduce noise?
In my experience with several ADCs, the ADC can take a surge of current when initially calculating a sample. This can modify the voltage at the input i.e. there is the possibility of a measurement error.

These types of ADCs are referred to as charge-redistribution successive-approximation devices or sometimes switched-capacitor ADCs: -



Analog Devices source here.

Adding a capacitor at the input means that this surge of current does not significantly "alter" the voltage being measured because the external capacitor chosen at the input is many times the value of the internal capacitors.

The AD source above describes how the effect can also compromise the reference voltage and this, of course, is also relevant to protecting the integrity of the input signal.


  I'm trying to figure out how Cdiff helps reduce noise/improve things.


It also does what you say in your question i.e. it will reduce mismatch between the two CM capacitors but I would say that this is secondary to its main purpose.