This work addresses the stabilization of hydrogen flames inside porous media. Hydrogen is a peculiar fuel with a large molecular diffusivity, triggering preferential diffusion and other effects related to non-unity Lewis numbers. Consequently, the macro-scale behavior of hydrogen flames is highly influenced by the flame-wall interactions at the pore-scale. In this study, direct pore-level simulations are used for the investigation of anchoring mechanisms and burning-rate enhancement for lean hydrogen flames embedded in inert porous media. It is observed that preferential diffusion greatly enhances flame anchoring, in the wake of the struts, leading to a high increase in flame surface. Also, the local heat release rate is enhanced not only by the higher gas temperature resulting from the heat recirculation but also by the higher local equivalence ratio resulting from preferential diffusion. Furthermore, most of the heat produced by a hydrogen flame is released by the hydroperoxyl reactions, effective at low temperatures but necessitating radicals, mostly H. These radicals are produced by the shuffle reactions, effective at higher gas temperatures. The coupling between those two reaction groups is very dependent on the transport of radicals, which can be impacted by the pore scale velocity gradient, leading to hydrodynamic dispersion and flame wrinkling. Consequently, it is shown that the burning-rate enhancement observed within porous burners fueled with hydrogen is not only due to heat recirculation but also to increased transports of radicals and preferential diffusion effects, which should be accounted for in macroscopic models.