The genetic architecture of skull shape has been extensively studied in mice and the results suggest a highly polygenic and additive basis. In contrast few studies have explored the genetic basis of the skull variability. Canalization and developmental stability are the two components of phenotypic robustness. They have been proposed to be emergent properties of the genetic networks underlying the development of the trait itself, but this hypothesis has been rarely tested empirically. Here we use outbred mice to investigate the genetic architecture of canalization of the skull shape by implementing a genome-wide marginal epistatic test on 3D geometric morphometric data. The same data set had been used previously to explore the genetic architecture of the skull mean shape and its developmental stability. Here, we address two questions: (1) Are changes in mean shape and changes in shape variance associated with the same genomic regions? and (2) Do canalization and developmental stability rely on the same loci and genetic architecture and do they involve the same patterns of shape variation? We found that unlike skull mean shape, among-individual shape variance and fluctuating asymmetry (FA) show a total lack of additive effects. They are both associated with complex networks of epistatic interactions involving many genes (protein-coding and regulatory elements). Remarkably, none of the genomic loci affecting mean shape contribute these networks despite their enrichment for genes involved in craniofacial variation and diseases. We also found that the patterns of shape FA and individual variation are largely similar and rely on similar multilocus epistatic genetic networks, suggesting that the processes channeling variation within and among individuals are largely common. However, the loci involved in these two networks are completely different. This in turn underlines the difference in the origin of the variation at these two levels, and points at buffering processes that may be specific to each level.