Transport of hydrogen in hydrous minerals under high pressure is a key step for the water cycle within the Earth interior. Brucite Mg(OH) 2 is one of the simplest minerals containing hydroxyl groups and is believed to decompose under the geological condition of the deep Earth's mantle. In the present study, we investigate the proton diffusion in brucite under high pressure, which results from a complex interplay between two processes: the O-H reorientations motion around the c axis and O-H covalent bond dissociations. First-principle path-integral molecular dynamics simulations reveal that the increasing pressure tends to lock the former motion, while, in contrast, it activates the latter which is mainly triggered by nuclear quantum effects. These two competing effects therefore give rise to a pressure sweet spot for proton diffusion within the mineral. In brucite Mg(OH) 2 , proton diffusion reaches a maximum for pressures close to 70GPa, while the structurally similar portlandite Ca(OH) 2 never shows proton diffusion within the pressure range and time scale that we explored. We analyze the different behavior of brucite and portlandite, which might constitute two prototypes for other minerals with same structure. Hydroxide minerals play an important role in several problems in geology, surface science or for industrial applications. Among them, brucite Mg(OH) 2 can be formed at the interface between periclase MgO and water at ambient conditions 1-3. The trigonal brucite structure consists of alternating layers along the c axis that terminate with hydroxyls (Fig. 1). This structure is common to other hydroxides of divalent metals, such as Ca(OH) 2 , Ni(OH) 2 and Cd(OH) 2. Portlandite Ca(OH) 2 is the main component of cements and concretes, which motivated a large number of investigations about its elastic properties. Because of their anisotropic structure, brucite iso-structural minerals are much more compressible along the c axis than in the other two directions, parallel to the stacks. Mg(OH) 2 can also act as a water vector in subduction zones, through complex processes that take place within the Earth interior 4,5. Therefore, the behavior of brucite and brucite-like minerals at very high pressure has been widely investigated. X-ray diffraction of Mg(OH) 2 up to 78 GPa showed that the c a / ratio decreases steadily from ambient pressure up to about 25 GPa and then stays almost constant 6. Those results suggest that the properties of brucite at very high pressure, and in particular the nature of the inter-layer bonding, could differ significantly from ambient conditions. Moreover, the hydroxyl groups that are parallel to the c axis at ambient conditions slant in three equivalent positions as the inter-layer distance shrinks even under moderate pressure 7 or when decreasing temperature 8. Besides reducing the global symmetry from P m 3 1 down to P3, the slanted OH groups can significantly alter several physical properties of brucites. Firstly, it could allow for the formation of hydrogen bonds between the layers 9 , which eventually reinforce under further compression and modify the compressibility along c 10. Secondly, when the protons form a non null θ angle with the c axis, they cannot arrange in a static ordered structure. Such proton disorder, which is closely related to proton frustration 11,12 , has also been invoked as the reason for the pressure-induced hydrogen sublattice amorphization in brucites 7,13. The existence of a quasi two-dimensional proton liquid in those extreme conditions can be conjectured, but the properties of the whole structure, if stable, have so far escaped a precise characterization. In particular, the occurrence of proton hopping is plausible, but whether this process results in a long-range diffusion is a totally open question. From the theoretical viewpoint, the previous observations call for a dynamical treatment of the proton arrangement within the brucite structure at high pressure. Moreover, in such conditions nuclear quantum effects, that is, all the properties that go beyond a purely classical description of ion dynamics 14 , such as zero-point