The building of effective neural network architectures for solving image compressive sensing (CS) problems is a challenge. Hence, it is helpful to consult the structural insight provided by traditional optimization algorithms, the results of which are interpretable. Inspired by this concept, we propose a fast, light, easily interpreted, and relatively stable learning-based method for solving image CS problems. This method is termed the Generalized ProXimal Alternating Direction Method of Multipliers Network (GPX-ADMM-Net) and can be used to solve image CS problems that conventionally are solved using optimization algorithms with intensive computations. GPX-ADMM-Net features the following characteristics: (1) It achieves a higher or comparable performance with state-of-the-art learning-based methods for the image CS problem in terms of reconstruction quality, running speed, and storage cost. (2) Because our method strictly follows the insight of optimization algorithms, it possesses a measurement rate (MR) adaptivity able to reconstruct acceptable image qualities under different MRs with only a single set of trained parameters, which is a unique property in learning-based methods. (3) Despite its dedicated design for the image CS problem, it possesses a cross-task adaptivity extended to handle other image inverse problems ( e.g. , super-resolution and inpainting) that are treated as a special case of CS. Extensive experimental results validate the above claims.