Diesel is refined oil. Some run their diesel on Waste Motor Oil, WMO, and so yeah it will burn it as it can and just throw the rest out the exhaust. I would be looking at doing a compression check, and monitor the oil level like a hawk. Something is not right there.
You may also have bad seals on the valve stems and it is leaking down into the cylinder(s) at that point. That would be the most likely in my mind. An exhaust seal is gone and the oil is just being blown out by the air of the cylinder.