Option one, with approximately 98% probability, is "fail hard". A few geeks will run nodes and brag about it on places like HN, and that'll be it.
Option two is that Diaspora succeeds, which will require some way around making everyone run their own node; basically, some company with the infrastructure to step in and host services for people, for cheap or preferably free. If an existing company -- one which already offers services most people use -- were to do this and make it easy enough, they'd probably end up running a huge percentage of Diaspora.
What sort of company would do that, you ask? Why, the company which already has all the info Facebook doesn't know about you, and would love to get access to the info Facebook does. You know, that search engine with the colorful logo.