From the article posted above.
"The first form of asexual reproduction is "budding", which can be seen when a small growth arises from the lower edge of a specimen's flesh. This growth can increase in size over time, and can eventually develop a small skeleton of its own. As it gets larger and heavier it will sag down, and eventually drop away, coming to rest somewhere and attaching to the substrate (Borneman 2001 and Fossa & Nilsen 1998). In aquariums, hobbyists can often speed things up a bit by clipping off buds before they drop, and can then place them in an appropriate location.
While this sort of budding is also typical of many other types of coral, the second method these particular species employ is quite unusual. Unlike many other corals with similar skeletal structures, the flesh of the bubble corals can wrap up and over the top of the skeleton and sometimes all the way down the sides, too. When it does, the soft tissue can actually spread out and over adjacent areas of substrate, as well. Then, such extensions of tissue can, at times, give rise to a whole new coral (Borneman 2001)."