On diesel engines a worn in-line injection pump is a very typical cause of high oil consumption. The moving parts of the fuel injection pump are lubricated by the engine oil. When elements of the oil pump get worn, engine oil can enter working chambers of the pump elements between the cylinder and the piston of the pump.
This usually happens during the downward stroke of the pump piston by the vacuum created in the chamber. The vacuum sucks in the engine oil mixing it with the diesel fuel and injects it to the combustion chamber, where it is burnt.