Mushrooms and many soft corals feed by absorption of nutrients from the water column. You can't feed them directly.
However, if you have soft corals with polyps, some of those need size appropriate food -- but not all. Sarcophyon, for example, has polyps but doesn't use them to feed.
In a nutshell, glauuds answer was correct -- fish poop! With soft corals, a higher bioload than a stoney coral tank, some dissolved organics and a low level of nitrates will make them happy.