Leakage current effect?

For a typical diode used in a psu rectifier role, the leakage current has virtually no importance here, even from an extreme purist audiophile point of view, the leakage current is usually in the range of uA, ie. somewhere one millionth of an Ampere and a static phenomenon, it's as if you would put a mega ohm range resistor in parallel with the diode.

The type of noise usually of concern and associated with psu diodes is related to the switch-off behavior, ie. the Reverse Recovery Time + the rate of change of the voltage over the diode, not the static leakage currents or broad band noise which is a much lesser problem (except Zener diodes which are quite noisy and of natural reasons also dependent on the chosen zener voltage).
That is because diodes don't turn off instantaneously, so there's a very brief moment it conducts in reverse mode as well until the diode has fully turned off (going into full reverse recovery), this brief 'hiccup' is happening only at the moment when the voltage applied over the diode is reversing from forward conduction to reverse mode, not the other way.

But for sinusoidal 50 or 60 Hz mains voltage this is usually not a cause of problem for a fast recovery diode such as schottky diodes as the voltage change is relatively very slow, in SMPS (Switch Mode Power Supply) where schottky diodes are usually used the voltage change is much much grater and causes not only challenging EMC problems (both conducted and emitted noise) but also loss of efficiency and heat problem.

As for the choice of "audiophile grade" diodes for mains powered psu's you may want to look at "Soft Recovery" diodes to have some peace of mind. :-)

https://www.electronics-tutorials.ws/diode/diode_3.html
https://en.wikipedia.org/wiki/Diode
https://en.wikipedia.org/wiki/Schottky_diode

ps: You could go even further to improve the switch-off noise by adding an RC-series snubber circuit in parallel with the diode.
 
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