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Deep neural networks (DNN) have achieved great success in image restoration. However, most DNN methods are designed as a black box, lacking transparency and interpretability. Although some methods are proposed to combine traditional optimization algorithms with DNN, they usually demand pre-defined degradation processes or handcrafted assumptions, making it difficult to deal with complex and real-world applications. In this paper, we propose a Deep Generalized Unfolding Network (DGUNet) for image restoration. Concretely, without loss of interpretability, we integrate a gradient estimation strategy into the gradient descent step of the Proximal Gradient Descent (PGD) algorithm, driving it to deal with complex and real-world image degradation. In addition, we design inter-stage information pathways across proximal mapping in different PGD iterations to rectify the intrinsic information loss in most deep unfolding networks (DUN) through a multi-scale and spatial-adaptive way. By integrating the flexible gradient descent and informative proximal mapping, we unfold the iterative PGD algorithm into a trainable DNN. Extensive experiments on various image restoration tasks demonstrate the superiority of our method in terms of state-of-the-art performance, interpretability, and generalizability. The source code is available at https://github. com/MC-E/Deep-Generalized-Unfolding-Networks-for-Image-Restoration.