Ice in cold cosmic environments is expected to be organized in a bilayered structure of polar and apolar components. The initial water-rich layer is embedded in an icy CO envelope, which provides the feedstock for methanol formation through hydrogenation. These two components are thought to be physically segregated, unless an increase in temperature favors mobility and reactivity within the ice. We present new and robust evidence of X-ray-induced diffusion within interstellar ice analogues at very low temperatures, leading to an efficient mixing of the molecular content of the ice. The results of our study have two main implications. First, molecular mixing enhances chemical reactions from which complex organic species, including many of prebiotic interest, are formed. Second, diffusion drives the desorption of species that would otherwise remain buried near the surface of dust, thus enhancing their abundances in the gas, where they can be detected in the radio-wave domain. Such a scenario may have implications for the chemical history of ices in protoplanetary disks, in particular in the early stages of their life.