1993 Ford F350 Truck cuts out when the accelerator is press

I have a 93 Ford f350 four door 1 ton single wheel truck. I drives okay when you are taking it nice and slow on the accelerator. I mean, you really have to take it slow. If you press on the accelerator rapidly or not even so rapidly, the truck starts to sputter, and sometimes, you can floor it and it is like it loses all fuel flow or something, because the truck will absolutely stop accelerating, and as long as you have it floored, the truck will just roll until it would eventually come to a stop. However, sometimes, you can stomp it to the floor and you would not have a problem at all. I have replaced the fuel pump, fuel filter, and fuel regulator. What could this problem be? Could it be the injectors? Can the injectors be cleaned? I do not know if it has anything to do with this problem or not, but, also the truck idles extremely fast when put into park.