Interactive human motions and the continuously changing nature of intentions pose significant challenges for human trajectory prediction. In this paper, we present a neuralized Markov random field (MRF)-based motion evolution method for probabilistic interaction-aware human trajectory prediction. We use MRF to model each agent's motion and the resulting crowd interactions over time, hence is robust against noisy observations and enables group reasoning. We approximate the modeled distribution using two conditional variational autoencoders (CVAEs) for efficient learning and inference. Our proposed method achieves state-of-the-art performance on ADE/FDE metrics across two dataset categories: overhead datasets ETH/UCY, SDD, and NBA, and ego-centric JRDB. Furthermore, our approach allows for real-time stochastic inference in bustling environments, making it well-suited for a 30FPS video setting. We open-source our codes at: https://github.com/AdaCompNUS/NMRF_TrajectoryPrediction.git