Some researchers in Spain are talking about a new engine that runs on pure oxygen and a hydrocarbon fuel. From the limited info I've been able to find, their real innovation in a ceramic matrix that lets oxygen in and keeps nitrogen out. The NOx-free engine appears to be entirely theoretical at this point.
In some ways it sounds similar to the Allam cycle being used by NetPower. They are using CO2 as a working fluid in a gas turbine because CO2 has a higher n than Nitrogen which leads to a higher thermal efficiency for the gas turbine. NetPower thinks that the higher thermal efficiency will offset the expense of isolating the oxygen from the atmosphere.
So, back to the guys in the Spain. Their press releases are very sparse. They have almost no details on their engine. I suspect they haven't gotten much further than the oxygen separation membrane. I'm wondering if their engine will have/need some sort of CO2 recirculation system like NetPower to give their engine more working fluid. It's been too long since I've done thermo on engine cycles to work out what the efficiency/power density of a pure oxygen-diesel cycle would be. Could you downsize the displacement without all that pesky Nitrogen in the way? Or do you need the extra mass to absorb some of the energy keep things from getting too hot in the cylinder?