We can speculate all we want, but until then, well...
Much speculation rests on the Black Soulstone. We think it somehow taps into the Abyss, where the souls of Mephisto, Diablo and Baal were sent upon their deaths. The Abyss is the nether realm from which nothing emerges. Supposedly.
Anyways. The Black Soulstone was created by a member of the Horadrim, Zoltun Kulle, and was made to imprison the souls of Demons and Angels alike. Now, Azmodan is searching for this, which would give him the power of all the other Prime Evils, since they've mostly all been killed off and sent to the Abyss. It could be from this demonic amalgamation of souls, coupled with the fact that... something something something (spoiler:
Leah is, through the Dark Wanderer, Diablo's daughter)... that Diablo manifests as the strongest-willed demon.
So, that's the theory we're running with now. Help any?