What about bulk? A battery sized unit isn't that big of a deal in a car. I'm curious more than anything else, since nothing really gets explained these days, just: AWESOME NEW REVOLUTIONARY ACRONYM!
Are you talking about a gasoline direct injection pump? The gasoline DI pumps are very compact, there is not much to them. Most of them are just a spring-loaded plunger that is operated by an extra cam lobe somewhere, they're built into the cylinder head. There is a pressure regulator, and pipes taking the fuel to the injectors. The injectors go straight into the head, usually between the two intake valves, instead of into the intake runner. Doesn't really take up appreciably more space than a standard low-pressure port injection system ... but it certainly costs more, and I'm not aware of any DI systems that are capable of functioning at much higher revs than car engines see (say, 8000-ish).
The diesel common-rail pumps are bigger, and are generally a complete unit unto themselves, not something screwed into the cylinder head. But they run at much higher pressure and need to be a lot more robust because of that. Standard gasoline port injection runs at around 3 bar pressure. Gasoline direct injection, around 200 bar. Diesel common-rail, around 2000 bar.