0.01pF is an impossibly small value, I think that you mean 0.01µF (10,000pF).
The practice comes from the early days of silicon diodes, they were put there to absorb fast high voltage spikes which could kill the diode.
Also, when several diodes were connected in series to give a higher voltage rating, it was common to put resistors (100kΩ) in parallel with each diode to equalise the reverse voltage across each diode when it was not conducting, sometimes a capacitor was put in parallel with each resistor as well.
As Uncle $crooge noted it can reduce noise that can be radiated or conducted into audio circuitry. Some diodes have an abrupt reverse voltage turn-off which can excite parasitic oscillations in any stray reactances and generate noise harmonics. This diode feature is exploited in some types of harmonic frequency generators to generate a higher frequency from a low frequency. In this case the capacitors smooth the abrupt turnoff and suppress the harmonics.