Exactly what the title asks. "Diode" comes with it the ideas of depletion layers and forward/reverse biasing and electron-hole recombination, but SPAD physics doesn't seem to be dependent on any of that. You just put a giant electric field on, and as soon as a photon comes and promotes a charge to the conduction band, it gets so much energy that it can knock other electrons out of their atoms, creating the avalanche.
In other words the fact that it's "reverse-biased" relative to the doping of the semiconductors seems irrelevant, as does the fact that the reverse-bias is above the breakdown voltage.
Could I take a piece of undoped silicon and use it as a SPAD if I put a sufficiently large voltage on it? Or else why is it important that it's a diode?