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In advanced metering infrastructure (AMI), smart meters (SMs), which are installed at the consumer side, send fine-grained power consumption readings periodically to the electricity utility for load monitoring and energy management. Change and transmit (CAT) is an efficient approach to collect these readings, where the readings are not transmitted when there is no enough change in consumption. However, this approach causes a privacy problem that is by analyzing the transmission pattern of an SM, sensitive information on the house dwellers can be inferred. For instance, since the transmission pattern is distinguishable when dwellers are on travel, attackers may analyze the pattern to launch a presence-privacy attack (PPA) to infer whether the dwellers are absent from home. In this paper, we propose a scheme, called "STDL", for efficient collection of power consumption readings in AMI networks while preserving the consumers' privacy by sending spoofing transmissions (redundant real readings) using a deep-learning approach. We first use a clustering technique and real power consumption readings to create a dataset for transmission patterns using the CAT approach. Then, we train an attacker model using deep-learning, and our evaluations indicate that the success rate of the attacker is about 91%. Finally, we train a deep-learning-based defense model to send spoofing transmissions efficiently to thwart the PPA. Extensive evaluations are conducted, and the results indicate that our scheme can reduce the attacker's success rate, to 13.52% in case he knows the defense model and to 3.15% in case he does not know the model, while still achieving high efficiency in terms of the number of readings that should be transmitted. Our measurements indicate that the proposed scheme can reduce the number of readings that should be transmitted by about 41% compared to continuously transmitting readings.