I'm struggling with the same reasoning: NOx is the result of high combustion temperatures, which is a pure function of the compression ratio (and fuel mixture), which is the thing that defines the high efficiencies you can get with a diesel cycle.

The argument in the linked wikipedia entry is that combustion temperatures are lower in this cycle because the better fuel/air mixing means it can burn much leaner and thus at a lower temperature. But a leaner mixture means lower power for a given displacement too, which means lower efficiency than a comparable traditional diesel (which are already hard-pressed to see gains like the 40% claimed against well-tuned gas engines).

Honestly the whole thing sounds very snake oily to me. I don't deny that it's possible such a thing could be tuned to operate as well as a traditional engine, but... it sounds awfully fiddly. I'd want to see numbers from a production engine in a real car before placing any bets. Electric continues to look like a much better bet to my eyes.