What sources of randomness does the brain use for sampling?
Not sure if I am getting your question right. You are asking for noise that has an inherently information processing function? I would add an other aspect of noises

Noise as an emerging property


On a large scale, when massive amounts of neurons are
synchronising, then you can detect Noise with Electrodes, like in
the case of EEG. EEG follows an 1/f² or 1/f³ law (brownian
noise, red noise, pink noise, depending on the literature). This
principle can be found anywhere in the world. It states that higher
frequencies / faster oscillating signals have increasingly smaller
amplitudes, similar to smaller and larger waves on the sea and so
on.
In this case is noise a byproduct of other (stochastic) processes.
On a small scale, which would probably be something you would
    measure by using 'clamping'-technique on single neurons.  The
    firing rate of a neuron (a neuron chemically charging, until it
    reaches a threshold, which turns into a all-or-nothing case) also
    follows some 'systematic randomness' on which probabilistic,
    stochastic and noisy properties might be useful to describe these
    processes.
    In this case is noise a property that emerges from natural stochastic single-neuron firing processes.


Noise emerging from signals related to certain anatomic sources


In how far I remember (I do not have a good resource on that) the
    hippocampus, which is highly relevant for memories, has a strong randomization aspect inherently in its functioning. 
    This might be my closest guess to your question?!
Another very distinct 'stochastic' process created by the
Thalamus, a largely dominant, pace-giving rhythm within the brain.


Ressource: Buszaki Rhythms of the Brain is a nice read on various of these topics

On noise as an error process

Maybe I got your question a little wrong, but thinking of the brain that in the run of evolution turned out to be highly efficient and energy saving, does not want to have any noise that does not fulfill any purpose. (But as I understand, your question was related to the functional aspect of noise.)