Nuclear magnetic resonance (NMR) is used in geological characterization to investigate the internal structure of geomaterials filled with fluids containing 1H and 13C nuclei. Subsurface NMR measurements are generally acquired as well logs that provide information about fluid mobility and fluid-filled pore size distribution. Acquisition of subsurface NMR log is limited due to operational and instrumentation challenges. We implement a variational autoencoder (VAE) for improved training of a neural network (NN) to generate the NMR-T2 distributions along a 300-ft depth interval in a shale petroleum system at 11000-ft depth below sea level. Subsurface mineral and kerogen volume fractions, fluid saturations, and T2 distributions acquired at 460 discrete depth points were used as the training data set. The trained VAE-NN successfully predicts the T2 distributions for 100 discrete depths at an $R^{2}$ of 0.75 and normalized root-mean-square deviation of 15%.