In this work, a multi-mode combustion model, that combines a comprehensive kinetics scheme for volumetric heat release and a level-set-based model for turbulent flame propagation, is applied over the range of engine combustion regimes from non-premixed to premixed conditions. Model predictions of the ignition processes and flame structures are compared to measurements from the literature of naturally occurring luminous emission and OH planar laser induced fluorescence (PLIF). Comparisons are performed over a range of conditions from conventional diesel operation (i.e., short ignition delay, high oxygen concentration) to a low temperature combustion mode (i.e., long ignition delay, low oxygen concentration). The multi-mode combustion model shows excellent prediction of the bulk thermodynamic properties (e.g., rate of heat release), as well as local phenomena (i.e., ignition location, fuel and combustion intermediate species distributions, and flame structure). The results of this study show that even in the limit of mixing controlled combustion, the flame structure is captured extremely well without considering sub-grid scale turbulence-chemistry interactions. The combustion process is dominated by volumetric heat release in a thin zone around the periphery of the jet. The rate of combustion is controlled by transport of reactive mixture to the reaction zone and the dominant mixing processes are well described by the large scale mixing and diffusion. As the ignition delay is increased past the end of injection (i.e., positive ignition dwell), both the simulations and optical diagnostics show that the reaction zone spans the entire jet cross-section. In this combustion mode the combustion rate is no longer limited by transport to the reaction zone, but rather by kinetic timescales. Although comparisons of results with and without consideration of flame propagation show very similar flame structures and combustion characteristics, the addition of the flame propagation model reveals details of the edge or triple-flame structure in the region surrounding the diffusion flame at the lift off location. These details are not captured by the purely kinetics based combustion model, but are well represented by the present multi-mode model.