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While traditional statistical signal processing model-based methods can derive the optimal estimators relying on specific statistical assumptions, current learning-based methods further promote the performance upper bound via deep neural networks but at the expense of high encapsulation and lack adequate interpretability. Standing upon the intersection between traditional model-based methods and learning-based methods, we propose a model-driven approach based on the maximum a posteriori (MAP) framework, termed as MDNet, for single-channel speech enhancement. Specifically, the original problem is formulated into the joint posterior estimation w.r.t. speech and noise components. Different from the manual assumption toward the prior terms, we propose to model the prior distribution via networks and thus can learn from training data. The framework takes the unfolding structure and in each step, the target parameters can be progressively estimated through explicit gradient descent operations. Besides, another network serves as the fusion module to further refine the previous speech estimation. The experiments are conducted on the WSJ0-SI84 and Interspeech2020 DNS-Challenge datasets, and quantitative results show that the proposed approach outshines previous state-of-the-art baselines.