Al was correct about 'pushing' with Diafine, but I think a little more explanation might be in order...
The term 'push processing' simply means over-developing the film. By the same token, 'pull processing' is under-developing the film.
Most developers continue to develop the film until they are stopped from doing so, by stop bath or fix. They just keep on keepin' on, until you make them quit it.
This is good. It lets us under-expose and over-develop and get more-or-less properly-exposed negatives. Yay, us.
Diafine is NOT a push processing developer. It does NOT keep on keepin' on if you leave the film in it for too long. That is because Diafine is a two-part developer that 'develops to exhaustion'. The Part A developer seeps into the spongy emulsion like a sponge absorbs water, and when you pour the Part A out, the part that got sucked in to the film stays there. The Part B developer then attacks the film and doing its thing, but only as long as there is Part A for it to rub up against. When the Part A left in the 'spongy' gelatin emulsion is gone, it stops working. That is what we mean by 'to exhaustion'.
Diafine does not 'push' Tri-X to ISO 1200 and beyond. It has that effect, yes. But it is not a push. That is the normal speed of Tri-X in Diafine, that's all.
What that means in terms of Jack's original question is this - if you shoot Tri-X at EI 400 and process it in Diafine, you get very thick negatives, as Al said. They might be usable, especially if scanned with a dedicated film scanner.
Diafine is pretty forgiving, I've found. I don't make a habit of it, but if I find myself trying to get the last few shots of a roll in dying light and I've been exposing at EI 1200, instead of decreasing my shutter speed beyond what I can reasonably hand-hold, I'll just rate the last few frames at EI 1600 or even higher and I usually get something I can use in Diafine. I would not do that with Tri-X pushed to differing speeds on the same roll in any other developer.