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Plug-and-play denoisers can be used to perform generic image restoration tasks independent of the degradation type. These methods build on the fact that the Maximum a Posteriori (MAP) optimization can be solved using smaller sub-problems, including a MAP denoising optimization. We present the first end-to-end approach to MAP estimation for image denoising using deep neural networks. We show that our method is guaranteed to minimize the MAP denoising objective, which is then used in an optimization algorithm for generic image restoration. We provide theoretical analysis of our approach and show the quantitative performance of our method in several experiments. Our experimental results show that the proposed method can achieve 70x faster performance compared to the state-of-the-art, while maintaining the theoretical perspective of MAP.