This work presents an analysis of the stabilization of diffusion flames created by the injection of fuel into hot air, as found in Diesel engines. It is based on experimental observations and uses a dedicated Direct Numerical Simulation (DNS) approach to construct a numerical setup, which reproduces the ignition features obtained experimentally. The resulting DNS data are then used to classify and analyze the events that allow the flame to stabilize at a certain Lift-Off Length (LOL) from the fuel injector. Both DNS and experiments reveal that this stabilization is intermittent: flame elements first auto-ignite before being convected downstream until another sudden auto-ignition event occurs closer to the fuel injector. The flame topologies associated to such events are discussed in detail using the DNS results, and a conceptual model summarizing the observation made is proposed. Results show that the main flame stabilization mechanism is auto-ignition. However, multiple reaction zone topologies, such as triple flames, are also observed at the periphery of the fuel jet helping the flame to stabilize by filling high-temperature burnt gases reservoirs localized at the periphery, which trigger auto-ignitions.