Sponges are suspension feeders that use flagellated collar-cells (choanocytes) to actively filter a volume of water equivalent to many times their body volume each hour. Flow through sponges is thought to be enhanced by ambient current, which induces a pressure gradient across the sponge wall, but the underlying mechanism is still unknown. Studies of sponge filtration have estimated the energetic cost of pumping to be <1% of its total metabolism implying there is little adaptive value to reducing the cost of pumping by using "passive" flow induced by the ambient current. We quantified the pumping activity and respiration of the glass sponge Aphrocallistes vastus at a 150 m deep reef in situ and in a flow flume; we also modeled the glass sponge filtration system from measurements of the aquiferous system. Excurrent flow from the sponge osculum measured in situ and in the flume were positively correlated (r>0.75) with the ambient current velocity. During short bursts of high ambient current the sponges filtered two-thirds of the total volume of water they processed daily. Our model indicates that the head loss across the sponge collar filter is 10 times higher than previously estimated. The difference is due to the resistance created by a fine protein mesh that lines the collar, which demosponges also have, but was so far overlooked. Applying our model to the in situ measurements indicates that even modest pumping rates require an energetic expenditure of at least 28% of the total in situ respiration. We suggest that due to the high cost of pumping, current-induced flow is highly beneficial but may occur only in thin walled sponges living in high flow environments. Our results call for a new look at the mechanisms underlying current-induced flow and for reevaluation of the cost of biological pumping and its evolutionary role, especially in sponges.