That is a bit convoluted and contradictory. The greenhouse gases are (from most to least discharged) carbon dioxide, oxides of nitrogen (NOx), and methane plus a small percentage of halocarbons.
A highly efficient diesel engine might exhaust slightly less CO2 than an old clunker because it burns less fuel to produce the same amount of power but more efficient combustion also increases NOx emissions due to operating at higher temperature.
Soot or black carbon emissions are reduced when operating at higher temperatures but that increases NOx. Reducing combustion chamber temperature reduces NOx but it meas burning more fuel to achieve the same power and thereby increases CO2 emissions while at the same time it may increase soot and particulate emissions.
Aftertreatment systems to reduce soot and nitrous oxides (NO2) increase NOx because it raises the temperature of the gases in the aftertreatment catalyst. Adding selective catalytic reduction (SCR) to the aftertreatment system to reduce NOx means ammonia emissions and greenhouse gas emissions increase in the production of the urea reductant. Using exhaust gas recirculation to reduce NOx and soot increases fuell burn which increases CO2 emissions.
Going to natural gas fueled diesels may lead to increased NOx emissions as well as increased methane emissions.
There is no free lunch and converting one pollutant to another is in many cases a shell game.