At Sandia National Laboratories they had this same curiosity. They took a single cylinder version of the Caterpillar C10 and added a few sight glasses, mirrors and lasers to get a peak at what happens after the fuel is injected. One would think as soon as the fuel is injected into the hot chamber it would burn instantly. Not so. A lot happens. It is very complex.
One of the main things they are looking to achieve is low temperature combustion or homogeneous charge compression ignition (HCCI). With this method they can reduce NOx and PM at the same time without losing efficiency.