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Recent model-extraction attacks on Machine Learning as a Service (MLaaS) systems have moved towards data-free approaches, showing the feasibility of stealing models trained with difficult-to-access data. However, these attacks are ineffective or limited due to the low accuracy of extracted models and the high number of queries to the models under attack. The high query cost makes such techniques infeasible for online MLaaS systems that charge per query.We create a novel approach to get higher accuracy and query efficiency than prior data-free model extraction techniques. Specifically, we introduce a novel generator training scheme that maximizes the disagreement loss between two clone models that attempt to copy the model under attack. This loss, combined with diversity loss and experience replay, enables the generator to produce better instances to train the clone models. Our evaluation on popular datasets CIFAR-10 and CIFAR-100 shows that our approach improves the final model accuracy by up to 3.42% and 18.48% respectively. The average number of queries required to achieve the accuracy of the prior state of the art is reduced by up to 64.95%. We hope this will promote future work on feasible data-free model extraction and defenses against such attacks.