Recent work has explored integrating autoregressive language models with energy-based models (EBMs) to enhance text generation capabilities. However, learning effective EBMs for text is challenged by the discrete nature of language. This work proposes an adversarial training strategy to address limitations in prior efforts. Specifically, an iterative adversarial attack algorithm is presented to generate negative samples for training the EBM by perturbing text from the autoregressive model. This aims to enable the EBM to suppress spurious modes outside the support of the data distribution. Experiments on an arithmetic sequence generation task demonstrate that the proposed adversarial training approach can substantially enhance the quality of generated sequences compared to prior methods. The results highlight the promise of adversarial techniques to improve discrete EBM training. Key contributions include: (1) an adversarial attack strategy tailored to text to generate negative samples, circumventing MCMC limitations; (2) an adversarial training algorithm for EBMs leveraging these attacks; (3) empirical validation of performance improvements on a sequence generation task.