Nuclear magnetic resonance (NMR) logs can provide information on some critical reservoir characteristics, such as permeability, which are rarely obtainable from conventional well logs. Nevertheless, high cost and operational constraints limit the wide application of NMR logging tools. In this study, a machine learning (ML)-based procedure is developed for fast and accurate estimation of NMR-derived permeability from conventional logs. Following a comprehensive preprocessing on the collected data, the procedure is trained and tested on a well log dataset, with selected conventional logs as inputs, and NMR-derived permeability as target, shallow and deep learning (DL) methods are applied to estimate permeability from selected conventional logs through artificial production of NMR-derived information from the input data. Three supervised ML algorithms are utilized and evaluated, including random forest (RF), group method of data handling (GMDH), and one-dimensional convolutional neural network (1D-CNN). Additionally, a modified two-dimensional CNN (named as Residual 2D-CNN) is developed which is fed by artificial 2D feature maps, generated from available conventional logs. The hyper-parameters of the ML and DL models are optimized using genetic algorithm (GA) to improve their performances. By comparing the output of each model with the permeability derived from NMR log, it is illustrated that nonlinear machine and deep learning techniques are helpful in estimation of NMR permeability. The obtained accuracy of RF, GMDH, 1D-CNN and Res 2D-CNN models, respectively, is 0.90, 0.90, 0.91 and 0.97 which indicate that Res 2D-CNN model is the most efficient method among the other applied techniques. This research also highlights the importance of using generated feature maps for training Res 2D-CNN model, and the essential effect of the applied modifications (i.e., implementing residual and deeper bottleneck architectures) on improving the accuracy of the predicted output and reducing the training time.