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Exploration is a key challenge in Reinforcement Learning, especially in long-horizon, deceptive and sparse-reward environments. For such applications, population-based approaches have proven effective. Methods such as Quality-Diversity deals with this by encouraging novel solutions and producing a diversity of behaviours. However, these methods are driven by either undirected sampling (i.e. mutations) or use approximated gradients (i.e. Evolution Strategies) in the parameter space, which makes them highly sample-inefficient. In this paper, we propose a model-based Quality-Diversity approach. It extends existing QD methods to use gradients for efficient exploitation and leverage perturbations in imagination for efficient exploration. Our approach optimizes all members of a population simultaneously to maintain both performance and diversity efficiently by leveraging the effectiveness of QD algorithms as good data generators to train deep models. We demonstrate that it maintains the divergent search capabilities of population-based approaches on tasks with deceptive rewards while significantly improving their sample efficiency and quality of solutions.