Most sponges that I’ve looked into primarily consume Dissolved Organic Matter (DOM - sometimes called Dissolved Organic Carbon, or DOC, which is actually a component of DOM) and specific kinds of bacteria (which kinds vary at least a little from one sponge to another). Most of them seem to have no preference for where their DOC comes from, but they have a preference for algal-derived Dissolved Organic Nitrogen (i.e. DON produced by algae). Giant Barrel Sponges and some Boring Sponges have had their diets analyzed, and they primarily consume DOM (~80% of their total diet, with the remaining ~20% coming from Particulate Organic Matter (POM - primarily phytoplankton and bacteria, though, as mentioned above, bacteria is taken in much higher quantities than phyto). This ratio of approximately 80/20 seems to be pretty typical(though it can vary from what I've seen by +/-15% or so one way or another) for most sponges from what I can find.
Unfortunately, we don’t have an easy, hobbyist way to measure DOM, DOC, DON, or POM (or POC or PON) that I’m aware of, so we don't really have any way to determine if the sponges are getting enough food consistently to thrive (to say nothing of measuring the amounts of specific bacteria in our tanks), but there you have it.
