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Coherent imaging through scatter is a challenging task in computational imaging. Both model-based and data-driven approaches have been explored to solve the inverse scattering problem. In our previous work, we have shown that a deep learning approach can make high-quality and highly generalizable predictions through unseen diffusers. Here, we propose a new deep neural network (DNN) model that is agnostic to a broader class of perturbations including scatterer change, displacements, and system defocus up to 10X depth of field. In addition, we develop a new analysis framework for interpreting the mechanism of our DNN model and visualizing its generalizability based on an unsupervised dimension reduction technique. We show that our DNN can unmix the scattering-specific information and extract the object-specific information so as to achieve generalization under different scattering conditions. Our work paves the way to a highly robust and interpretable deep learning approach to imaging through scattering media.