Diffusion plays an important role in the properties of solids, which governs the kinetics of microstructural changes and processes of mass transport. The diffusional phenomena are most widespread in metals, alloys, and metastable and chemically complex solid solutions, mainly at elevated temperatures. For instance, the kinetics in metastable phases, such as oxidation, mixing, intermixing, thermal decompositions, and phase formation, are attributed to the diffusional rearrangement of atoms. Atomistic simulations have provided unprecedented insight into various material properties, with ab initio calculations, in particular, being highly successful in raising the level of understanding close to that of experimental observations. However, diffusion dynamics have been challenging due to the time scale limitation of ab initio molecular dynamics for the infrequent event of jump processes. In contrast, the nudged elastic band method (NEB) based on the transition state theory (TST) can be employed to overcome this shortcoming. This method can calculate the 0 K migration energy barrier of a diffusion process from a static density functional theory (DFT) calculation and the finite temperature diffusion quantities by considering the free energy contribution from phonon. However, the model of an amorphous system, considering the size limitation of ab initio methods to a few hundred atoms, is not large enough to represent real materials. Hence, one needs to consider the large-scale atomistic simulations to predict the properties accurately. In the present thesis, we present the mass transport-related phenomena in B1 nitride coatings using the diffusion migration barriers by the 0 K NEB calculations. In part of the thesis, we use phonon thermodynamics to extend the 0 K calculations to quantify the diffusion of the finite temperatures and pressures (pre-exponential coefficients and activation energies). Further, we train a machine learning interatomic potential (MLIP) and use it in large-scale molecular dynamics to study the structural and elastic properties of amorphous silicon nitrides. Many chemical environments in B1 nitride solid solutions provide a different value of vacancy formation energy and migration energy barriers, namely an "envelope". We use the envelope method to predict phase formation in ternary nitrides. Furthermore, we establish a relation between lattice distortion and sluggish diffusion in high-entropy nitrides (HEN) using the envelope methods.