This paper makes a comparative study on the normal diffusion flame (NDF) and inverse diffusion flame (IDF) characteristics of dimethyl ether (DME) in microgravitational spherical diffusion flame geometry by simulations with detailed fuel chemistry and a transport model. It is found that there always existed two combustion modes (i.e., hot flame and cool flame) in either NDF or IDF condition. The combustion progress of hot flames was controlled by diffusive mixing, while that of cool flames was controlled by low-temperature competing kinetics. The cool-flame structure dynamics were far away from the chemical equilibrium. The low-temperature branching rate of DME was positively dependent on the oxygen level, while its termination rate was enhanced with the increasing temperature. Being rather distinct from the NDF counterpart, DME IDFs had the oxygen-enriched combustion feature in either hot- or cool-flame condition. Furthermore, DME hot-flame extinction was induced by thermal radiative loss, while the cool-flame extinction was induced especially by the decrease of the low-temperature branching rate. Compared with hot NDFs, it would be of less effectiveness to control the hot IDF combustion process by positive measures. However, combustion in the latter configuration was much more stable than the former. In either NDF or IDF geometry, the cool-flame chemistry could help to extend the fuel flammability range considerably, and the two-reaction-zone structure of cool flame was responsible for cool-flame stability. In addition, the IDFs had much better ignition performance than the NDF counterpart.