What is a word (possibly an adjective) for something that spreads (perhaps rapidly)? This would refer to a virus but without the obvious bad connotation.
The term Viral has been co-opted and is no longer considered only a bad connotation. The phrase going viral is generally considered a good thing(unless you are the one being embarrassed in the video or ad)
quickly and widely spread or popularized especially by person-to-person electronic communication
Infectious is my one-word answer.
I'm guessing that it's not absolutely essential to emphasise the "spatial" connotations of spread, though they're often present by implication in my offerings anyway.
I'm also guessing that the thing itself at least in part produces it's own momentum causing it to spread - we're talking more about something like a virus that spreads itself, rather than something like plaster being spread on a wall by a tradesman.
The process of spreading is proliferation. The adjective prolific is normally used of something that has already spread, but if OP doesn't mind sounding a bit "erudite", he can use proliferatory to describe something which has the potential to spread, even if it hasn't actually done so yet.
Propagate, "To cause to ... multiply by generation" or "To cause to spread to extend" (sic) or "To spread from person to person..." may serve. Also see its synonyms that include disperse, disseminate, spread.
Adjective epidemic means "Like or having to do with an epidemic; widespread", eg "Epidemic hysteria occurred upon the incumbent’s reelection."
Comment: Propagate and its synonyms mentioned above are verbs. If you want other word forms, clarify the question and indicate if you are looking for words to be used as spreading, growing, burgeoning would be used, or as ductile, malleable, miscible would be used, etc.
I would suggest contagious. It has a very similar meaning without a negative connotation.
pervade, verb [ with obj. ] (esp. of a smell) spread through and be perceived in every part of: a smell of stale cabbage pervaded the air.