Diesel fuel is injected in a dense stream near the center of the cylinder. In order for it to burn, the fuel molecules must migrate towards the air molecules on the outskirts of the cylinder, and vice versa. Traditionally, it has been difficult for Diesel's to burn all of the injected fuel; it would be insufficiently atomized and you'd get haze.
Gas engines can burn fuel faster and more completely, because by the time of ignition the fuel is dispersed homogenously with the air throughout the cylinder.
If you're doing it right, the propane is going to be evenly disbursed throughout the cylinder when it is ignited by the injected Diesel.
The theory behind propane injection is that even burning of the propane will allow for a more complete burn of the injected Diesel. How that happens is largely a subject of conjecture; combustion dynamics are really, really complicated and hard to figure out. It's debatable whether it happens at all, and some people have seen results and other's haven't.
Today's common rails are also a holy-crap bunch more efficient at atomizing injected fuel than anything in the past; injection pressures on my truck are 13k PSI and common rails are twice that. So any benefits that propane does have is a lot lower on newer vehicles.
The above is only the logic for using propane to achieve a higher thermodynamic efficiency, by burning more of the injected Diesel. That logic is a lot shakier than the logic of using propane for high performance.
In the case of using propane for power... Diesel engines have traditionally been limited by their injection technology. The pistons on a gas engine act as their own fuel delivery pumps; the faster the pistons go, the faster gas is drawn in, and that gas is automatically dispersed evenly with the air in the cylinder. But on a Diesel, you need to rely on an injection pump system that pressurizes each little bit of fuel.
The exponentially increasing difficulty of an injection pump to deliver fuel at RPM is one of the reasons why Diesels have traditionally been regulated to low RPM. Propane, or any fumigated fuel, is an easy way to circumvent restrictions of an injection system.
My truck, for instance, can only inject 400 HP worth of fuel. If I want to add more fuel than that, I either need a bigger injection system, or I go the easy route and add a lot of gaseous fumigated fuel into the air intake; I can flow as much fuel as I want into the intake for virtually free. Only problem there is that the fumigated fuel isn't 1000 octane, so it is going to start preigniting at a point and will take out my bottom end.