Recently there has been a lot of interest in non-autoregressive (non-AR) models for speech synthesis, such as FastSpeech 2 and diffusion models. Unlike AR models, these models do not have autoregressive dependencies among outputs which makes inference efficient. This paper expands the range of available non-AR models with another member called energy-based models (EBMs). The paper describes how noise contrastive estimation, which relies on the comparison between positive and negative samples, can be used to train EBMs. It proposes a number of strategies for generating effective negative samples, including using high-performing AR models. It also describes how sampling from EBMs can be performed using Langevin Markov Chain Monte-Carlo (MCMC). The use of Langevin MCMC enables to draw connections between EBMs and currently popular diffusion models. Experiments on LJSpeech dataset show that the proposed approach offers improvements over Tacotron 2.