Ni-based superalloys are materials utilized in high-performance services that demand excellent corrosion resistance and mechanical properties. Its usages can include fuel storage, gas turbines, petrochemistry, and nuclear reactor components, among others. On the other hand, hydrogen (H), in contact with metallic materials, can cause a phenomenon known as hydrogen embrittlement (HE), and its study related to the superalloys is fundamental. This is related to the analysis of the solubility, diffusivity, and permeability of H and its interaction with the bulk, second-phase particles, grain boundaries, precipitates, and dislocation networks. The aim of this work was mainly to study the effect of chromium (Cr) content on H diffusivity in Ni-based superalloys; additionally, the development of predictive models using artificial intelligence. For this purpose, the permeability test was employed based on the double cell experiment proposed by Devanathan–Stachurski, obtaining the effective diffusion coefficient (Deff), steady-state flux (Jss), and the trap density (NT) for the commercial and experimentally designed and manufactured Ni-based superalloys. The material was characterized with energy-dispersed X-ray spectroscopy (EDS), atomic absorption, CHNS/O chemical analysis, X-ray diffraction (XRD), brightfield optical microscopy (OM), and scanning electron microscopy (SEM). On the other hand, predictive models were developed employing artificial neural networks (ANNs) using experimental results as a database. Furthermore, the relative importance of the main parameters related to the H diffusion was calculated. The Deff, Jss, and NT achieved showed relatively higher values considering those reported for Ni alloys and were found in the following orders of magnitude: [1 × 10−8, 1 × 10−11 m2/s], [1 × 10−5, 9 × 10−7 mol/cm2s], and [7 × 1025 traps/m3], respectively. Regarding the predictive models, linear correlation coefficients of 0.96 and 0.80 were reached, corresponding to the Deff and Jss. Due to the results obtained, it was suitable to dismiss the effect of Cr in solid solution on the H diffusion. Finally, the predictive models developed can be considered for the estimation of Deff and Jss as functions of the characterized features.