Diffusive Molecular Dynamics (DMD) is a class of recently developed computational methods for the simulation of long-term mass transport with a full atomic fidelity. Its basic idea is to couple a discrete kinetic model for the evolution of mass transport process with a non-equilibrium thermodynamics model that governs lattice deformation and supplies the requisite driving forces for kinetics. Compared to previous atomistic models, e.g., accelerated Molecular Dynamics and on-the-fly kinetic Monte Carlo, DMD allows the use of larger time-step sizes and hence has a larger simulation time window for mass transport problems. This dissertation focuses on the development, assessment and application of a DMD computational framework for the long-term, three-dimensional, deformation-diffusion coupled analysis of solute mass transport in nanomaterials. First, a computational framework is presented, which consists mainly of: (1) a computational model for interstitial solute diffusion, which couples a nonlinear optimization problem with a first-order nonlinear ordinary differential equation; (2) two numerical methods, i.e., mean field approximation and subcycling time integration, for accelerating DMD simulations; and (3) a high-performance computational solver, which is parallelized based on Message Passing Interface (MPI) and the PETSc/TAO library for large-scale simulations. Next, the computational framework is validated and assessed in two groups of numerical experiments that simulate hydrogen mass transport in palladium. Specifically, the framework is validated against a classical lattice random walk model. Its capability to capture the atomic details in nanomaterials over a long diffusive time scale is also demonstrated. In these experiments, the effects of the proposed numerical methods on solution accuracy and computation time are assessed quantitatively. Finally, the computational framework is employed to investigate the long-term hydrogen absorption into palladium nanoparticles with different sizes and shapes. Several significant findings are shown, including the propagation of an atomistically sharp phase boundary, the dynamics of solute-induced lattice deformation and stacking faults, and the effect of lattice crystallinity on absorption rate. Specifically, the two-way interaction between phase boundary propagation and stacking fault dynamics is noteworthy. The effects of particle size and shape on both hydrogen absorption and lattice deformation are also discussed in detail. / Ph. D. / Interstitial diffusion in crystalline solids describes a phenomenon in which the solute constituents (e.g., atoms) move from an interstitial space of the host lattice to a neighboring one that is empty. It is a dominating feature in many important engineering applications, such as metal hydrides, lithium-ion batteries and hydrogen-induced material failures. These applications involve some key problems that might take place over long time periods (e.g., longer than 1 s), while the nanoscale behaviors and mechanisms become significant. The time scale of these problems is beyond the capability of established atomistic models, e.g., accelerated Molecular Dynamics and on-the-fly kinetic Monte Carlo. To this end, this dissertation presents the development and application of a new computational framework, referred to as Diffusive Molecular Dynamics (DMD), for the simulation of long-term interstitial solute diffusion in advanced nanomaterials. The framework includes three key components. Firstly, a DMD computational model is proposed, which accounts for three-dimensional, deformation-diffusion coupled analysis of interstitial solute mass transport. Secondly, nu- merical methods are employed to accelerate the DMD simulations while maintaining a high solution accuracy. Thirdly, a high-performance computational solver is developed to implement the DMD model and the numerical methods. Moreover, regarding its application, the DMD framework is first validated and assessed in the numerical experiments pertaining to hydrogen mass transport in palladium crystals. Then, it is employed to investigate the atomic behaviors and mechanisms involved in the long-term hydrogen absorption by palladium nanoparticles with different sizes and shapes. The two-way interaction between hydrogen absorption and lattice deformation is studied in detail.