Advances in soft robotics and fluidic medical devices motivate the development of large, soft pumps that can efficiently pressurize and/or control volumes of fluid. Dielectric elastomer actuators (DEAs) have gathered recent interest due to their low cost, large strains, power efficiency, and high energy density. However, developing reliable, compliant electrodes for DEAs remains an open problem due to challenges with patterning robust conductors that do not appreciably stiffen the actuators. In this work, we present a method for utilizing fluid electrodes to drive an elastomeric diaphragm pump, where a dielectric elastomer membrane separates the internal fluid of the pump, which we connect to a power supply, from an external fluid connected to ground. Two one-way check valves govern the flow of fluid into and out of the internal chamber of the pump. When we apply a voltage to the internal fluid with respect to the external, grounded fluid, the electric field across the dielectric membrane induces an electrostatic force on the membrane, which compresses the membrane and causes it to expand outward, causing an increase in the volume of the internal chamber of the pump. This volume increase draws fluid in through the input check valve. When the electric field is removed, the elastic restoring force of the membrane returns the internal chamber of the pump to its original volume, forcing the excess fluid through the output check valve. This soft pump has a minimum of moving parts, operates silently, and obviates the need for the lubrication and maintenance required of traditional diaphragm pumps. This research opens the door for low-cost, silent, elastomeric pumps for biomedical or soft robotic applications, especially where excess noise, vibration, or contaminating materials are a concern.