A subsea pressure regulator includes: a spring housing; a spring disposed therein; a body having a bore formed therethrough and inlet and outlet ports; drive and balance adapters connected to opposite ends of the body; drive and balance plungers; and a supply seal assembly. Each plunger has: a piston shoulder engaged with the respective adapter, a first portion in fluid communication with an outlet chamber, and a second portion in fluid communication with ambient pressure. The supply seal assembly includes a seal carrier connected to the plungers and a seal bore formed therethrough. The spring biases the seal carrier toward an open position. The drive plunger is operable to move the seal carrier to a closed position in response to sufficient pressure in the outlet chamber overcoming the spring bias.