I haven't checked out that thread yet, so apologies if some of this is redundant.
Normal P-N junction diodes have a stored charge when conducting. When the polarity reverses this charge has to go somewhere before conduction stops and the diode blocks. The time it takes depends on the diode, current, circuit impedances, etc. It is usually quoted as a single number: the reverse-recovery time.
The way in which it dumps the charge can be very abrupt. Indeed, diodes are made specifically to maximize the high frequency energy in the event to generate harmonic energy---they are called step-recovery diodes.
There are diodes that recover quickly and uniformly to try for the best of both worlds, that is, fast efficient rectification but the lowest amount of harmonic energy consistent with that speed/efficiency. They are sometimes called soft-recovery diodes.
The problems come when (1) the energy radiates and conducts into neighboring circuits, (2) when the regulator and its capacitors don't reject/filter it enough. So, one common approach is to bypass the diodes with low-inductance caps---stacked films, multilayer ceramics, and so forth. But, what you are doing is mostly moving the resonant frequency of the local circuit down, and not so much dissipating the energy. You may even make things worse depending on how the lower frequency ringing couples into your system.
The usual case is when something ends up being inadvertently tuned to the emissions and has a nonlinear device like a bipolar base-emitter junction involved, which rectifies the r.f. bursts and gives rise to a buzz typically at the fundamental and harmonics of double the line frequency.
So to do a better job you can contrive a series r-c snubber, or even more elaborate networks. But you can also move the disturbance away, and minimize loop areas both for radiation and pickup. I had a case where 1N4003 diodes required series 47nF-30 ohms across each diode to keep the buzz out of another board a few inches away. It might have been fixed with a shield but the snubbers were simpler at the time.
The addition of the caps or snubbers has a disadvantage in that you are passing more line garbage on to the rest of the circuitry, so some people don't like them for this reason.
Schottky diodes have in principle no stored charge except due to the capacitances, but Pease points out that the structures of these usually have a little parasitic P-N action and associated stored charge. The new shining star among diodes is the silicon carbide schottky. At the moment they are only available as large geometry parts for switching power apps, especially power factor correction circuits. The are higher forward drop than metal-semi schottkies and normal P-N diodes, but they have unmeasureable reverse recovery time.
