No one knows yet. Some Scleronephthya seem to feed on phytoplankton, but even that will vary species to species. Otherwise, there is speculation that Dendros and Scleros use food sources ranging from microplankton, to bacteria, to direct chemical absorption; with any given species being very particular about which of these methods (if any) it can use. Unfortunatly, this is the main reason that "carnation corals" die 99.999% of the time in the hobby.