It's typical for sponges to grow in low lit areas. It sounds like your lighting isn't especially intense which makes it more plausible for there to be sponge growing on the underside so rapidly.

First pic and also halfway down the page looks exactly like yours:
http://www.wetwebmedia.com/lridfaq9.htm

They call it a Leather Latticework Sponge:
http://www.reefcentral.com/forums/sh....php?t=1777619

Here's a couple variations of the Leather Latticework Sponge (last pic):
http://www.myawesometank.com/wiki/in...brates.Sponges