A diesel engine works the same way as a gasoline engine except the compression ratio is twice as much and there's no ignition system as far as a spark being generated to ignite the mixture. The ignition of the fuel mixture is done by squeezing the air in the cylinder so much that a great amount of heat is created and than when diesel is sprayed in with the super heated air it's ignited to drive the piston down to turn the wheels of the vehicle. 

The diesel particulate filter [DPF] uses an oxidizing catalyst to control hydrocarbons.

Soot and larger sulfate particles are captured in the ceramic honeycomb of the DPF. Alternate passages of the honeycomb are plugged to form channels for the gases to pass through and trap particulates on the channel walls. To keep the particulates from filling the channels, a regeneration process is done to oxidize the carbon into carbon dioxide gas that will pass through the honeycomb. There are two types of regeneration: self - regeneration and forced regeneration. Self - regeneration takes place when the exhaust gases reach a temperature of about 1000*F oxidizing the carbon particulates. Forced regeneration is a function of the engine control computer that will use temperature sensors, throttle valve, intake heater and controller fuel delivery algorithms to cause a regeneration.