I'm new at this so bear with me, I have 2001 F-450 7.3 diesel. Driving the other day and the thing just cut off. Waited, started up got home and died again. The electric fuel pump (under hood) I replaced. But know it won't stay started. No fuel is staying in the motor. Doesn't make sense.

 

the fuel pump is on the frame rail under the cab. check the fuel filter and fuel psi.

 

Think you were messing with the fuel filter under the hood? Pump is under vehicle. Random stalling and restarting sounds like a classic CPS (camshaft position sensor) issue. This is a cheap and easy replacement part and common to fail. Could also be ICP or IPR. Or, I suppose, as you stated it could be the fuel pump. But, I doubt it.

 

Oh, also is your oil full? How old is the oil? 7.3's get a little finnicky with their oil!