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In Valence Change Memory (VCM) cells, the conductance of an insulating switching layer is reversibly modulated by creating and redistributing point defects under an external field. Accurate simulations of the switching dynamics of these devices can be difficult due to their typically disordered atomic structures and inhomogeneous arrangements of defects. To address this, we introduce an atomistic framework for modelling VCM cells. It combines a stochastic Kinetic Monte Carlo approach for atomic rearrangement with a quantum transport scheme, both parameterized at the ab-initio level by using inputs from Density Functional Theory (DFT). Each of these steps operates directly on the underlying atomic structure. The model thus directly relates the energy landscape and electronic structure of the device to its switching characteristics. We apply this model to simulate non-volatile switching between high- and low-resistance states in an TiN/HfO2/Ti/TiN stack, and analyze both the kinetics and stochasticity of the conductance transitions. We also resolve the atomic nature of current flow resulting from the valence change mechanism, finding that conductive paths are formed between the undercoordinated Hf atoms neighboring oxygen vacancies. The model developed here can be applied to different material systems to evaluate their resistive switching potential, both for use as conventional memory cells and as neuromorphic computing primitives.