A remarkable attribute of sponges is their ability to regrow an entire copy of their body from a tiny piece that has been separated from the original body. This describes one type of asexual reproduction in sponges called shedding. Shedding is the process in which sponges can slough off small pieces of their bodies that then grow into adult sponges. Shedding can be compared to paint chipping off, like what's happening in the picture. 

Poriferans, as well as Placozoans, are capable of reproducing asexually through budding.  The sponge has an outgrowth that grows until it's big enough to separate from the parent sponge.  Pictured is budding in yeast cells; the growing bud is almost as big as the parent cell and will soon separate.  If this were a sponge, once detached, the young sponge would attach itself to a hard surface to live out its life.

Some fresh-water sponges are able to form gemmules, which are clusters of amoebocytes covered in a protective coating.  These sponges form gemmules when the living conditions become harsh, such as cold temperatures, dryness, or lack of food.  The gemmule remains protected even if the rest of the sponge dies.  When environmental conditions improve, the gemmule grows into a new sponge.  Pictured is a cluster of amoebas.  How is this not quite a gemmule?  Think about the answer, then click "Show Me" to see if you are correct.

Gemmules are a cluster of amoebocytes, not amoebas. An amoeba is a unicellular organism in kingdom Protista. An amoebocyte is a type of cell located in a sponge. The amoebocytes resemble amoebas.