We have developed a CNN-based deep learning model for predicting the cation diffusivity through a 3D microstructure consisting of monodisperse spherical nanoparticles. The CNN approach not only achieves a high prediction accuracy, but also outperforms other physicsinspired deep learning models. We surmise that the latter is due to the ability of CNN filters to capture the relevant many-body spatial correlations not accounted for in the simple physics-based descriptors. On combining the trained CNN model with a simulated annealing algorithm for topology optimization, we achieve accelerated discovery of microstructures exhibiting ground truth diffusivities outside the domain of those observed for structures in the generated training dataset. Incorporating these additional observations to retrain the CNN model leads to further improvement in the prediction accuracy for a wide range of nanoparticle microstructures screened during the topology optimization runs. We observe a 41.3% increase in the maximum diffusivity compared to that in the initial training dataset generated using a combination of stochastic algorithm with physically intuited biasing. Ap-plying PCA to the dataset of structures revealed important physical features influencing cation diffusivity, thus providing a physical rationale for the performance of optimal morphologies. Such a data-driven analysis allows for a better interpretation of the quantitative effect of the cation transport model on the property of interest, i.e. cation diffusivity.