Chen and coworkers recently performed a Direct Numerical Simulation (DNS) of the constant volume ignition of a very lean hydrogen/air subject to different levels of temperature stratification [E. R. Hawkes, R. Sankaran, P. P. Pébay, J. H. Chen, Combustion and Flame 145(1-2): 145-159]. Under high levels of temperature stratification, two distinct modes of combustion are found: deflagrations and spontaneous ignition fronts. Deflagrations propagate in regions of high temperature gradient and low flame front curvature, while spontaneous ignition is associated with highly curved, low temperature gradient fronts. The simulations included hydrogen/air finite rate chemistry and molecular transport based on a Lewis number formulation for individual species. Differential diffusion effects are present for all temperature stratification cases and they become more pronounced as the level of stratification increases. At the highest level of temperature stratification tested, we find that differential diffusion has an impact on the overall heat release rate. By comparing simulations with and without differential diffusion, we find that differential diffusion has a twofold effect on the ignition event. Early in the ignition, regions with a hydrogen mass fraction higher than the nominal levels are created and they subsequently burn to achieve higher temperatures, which can be accounted for by simple equilibrium calculations. Later in the ignition process, differential diffusion enhances heat release rate in regions of high curvature where deflagrations are present, as generally expected in lean hydrogen/air premixed flames.