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We study submodular information measures as a rich framework for generic, query-focused, privacy sensitive, and update summarization tasks. While past work generally treats these problems differently ({\em e.g.}, different models are often used for generic and query-focused summarization), the submodular information measures allow us to study each of these problems via a unified approach. We first show that several previous query-focused and update summarization techniques have, unknowingly, used various instantiations of the aforesaid submodular information measures, providing evidence for the benefit and naturalness of these models. We then carefully study and demonstrate the modelling capabilities of the proposed functions in different settings and empirically verify our findings on both a synthetic dataset and an existing real-world image collection dataset (that has been extended by adding concept annotations to each image making it suitable for this task) and will be publicly released. We employ a max-margin framework to learn a mixture model built using the proposed instantiations of submodular information measures and demonstrate the effectiveness of our approach. While our experiments are in the context of image summarization, our framework is generic and can be easily extended to other summarization settings (e.g., videos or documents).