Here is an animated link showing the differances of the Otto and Diesel
cycles.

http://www.ulb.ac.be/sma/testcenter/...osedcycle.html

Notice the near instant burning in the example gives very nearly a
constant volume, in actual practice some compression is going on at
this time.

Also during a Diesel cycle it is hard to maintain a constant pressure,
it would actually drop off, especially near the end of the down stroke.