In various Web applications, users consume content in a series of sessions. That is prevalent in online music listening, where a session is a channel and channels are listened to in sequence, or in crowdsourcing, where a session is a set of tasks and task sets are completed in sequence. Content diversity can be defined in more than one way, e.g., based on artists or genres for music, or on requesters or rewards in crowdsourcing. A user may prefer to experience diversity within or across sessions. Naturally, intra-session diversity is set-based, whereas, inter-session diversity is sequence-based. This novel multi-session diversity gives rise to four bi-objective problems with the goal of minimizing or maximizing inter and intra diversities. Given the hardness of those problems, we propose to formulate a constrained optimization problem that optimizes inter diversity, subject to the constraint of intra diversity. We develop an efficient algorithm to solve our problem. Our experiments with human subjects on two real datasets, music and crowdsourcing, show our diversity formulations do serve different user needs, and yield high user satisfaction. Our large data experiments on real and synthetic data empirically demonstrate that our solution satisfy the theoretical bounds and is highly scalable, compared to baselines.