The hot or cold (whichever) valve is physically stuck open if turning off the supply faucet is the only way to stop the flow.
Could be a bit of debris obstructing the diaphragm or plunger from closing, as WashDaddy says, or some other internal problem. Replacing the assembly is the best sure way to fix the problem. Old-style valves could be disassembled for cleaning and even repair of internal parts, newer-style may be sealed.