It is not the pump, but the injector. Common rail systems dont use an injector pump as we typically understand it. On ford powerstrokes, you feed fuel at about 60PSI to the common fuel rail and all the injectors, very similar to a gas EFI system, a simple regulator dumps excess fuel back to the tank to maintain pressure on the rail.
The powerstroke has a high pressure engine oil/hydraulic pump that can push pressure to about 3500 PSI. It has a solenoid actuated regulator valve that is controlled/modulated by the ECU to regulate this oil pressure between about 500 and 3500 PSI. This high pressure engine oil is fed to all the injectors
The injectors are the key to the high pressure atomization. They are basically a combination of a hydraulic cylinder and a piston pump/syringe. They have electrically actuated hydraulic spool valves that open when commanded by the ECU to admit the 500-3500 PSI engine oil. The hydraulic cylinder piston face is 7 times larger than the injector piston face so the oil pressure is amplified into the fuel by a factor of 7. This gets you a variable injection pressure between 3500-24500 PSI. Injector pressure, firiing duration and timing are all controlled by the ECU.
Interesting system, I think they use the same ECU as the gas engine, but it feeds a second module instead of the injectors directly. The added module is called a fuel injection control module or FICM. It takes the injector firing commands from the ECU and converts them to the 48VDC used by the injector spool valves... works great, but is dependant on engine oil quality to maintain injector operation...