Some have been studied in lab settings and found to be herbivorous -
Aquilonastra corallicola, for example:
"
A. corallicola feeds on diatoms and green algae growing on the rock and glass walls of the aquaria."*
Others are thought to be either similar in diet to
A. corallicola or to be biofilm feeders. For what it's worth, though, even known herbivores like Chocolate Chip Starfish and Blue Linckia Starfish (both of which are currently thought - with good reason - by the scientific community to be biofilm-feeders) are known to exhibit opportunistic predation in aquaria, with Chocolate Chip Stars eating pretty much anything they can catch, and Blue Linckias being known to prey on Aquilonastra stars, sponges, tunicates, and even (very rarely) corals.
So, while these can be predatory, it would seem they either only go after specific corals for specific reasons (such as the coral having a specific biofilm/microbiome that attracts it), or that they use them as a last-resort famine food.
*Source: