The current advancements in open domain text generation have been spearheaded by Transformer-based large language models. Leveraging efficient parallelization and vast training datasets, these models achieve unparalleled text generation capabilities. Even so, current models are known to suffer from deficiencies such as repetitive texts, looping issues, and lack of robustness. While adversarial training through generative adversarial networks (GAN) is a proposed solution, earlier research in this direction has predominantly focused on older architectures, or narrow tasks. As a result, this approach is not yet compatible with modern language models for open-ended text generation, leading to diminished interest within the broader research community. We propose a computationally efficient GAN approach for sequential data that utilizes the parallelization capabilities of Transformer models. Our method revolves around generating multiple branching sequences from each training sample, while also incorporating the typical next-step prediction loss on the original data. In this way, we achieve a dense reward and loss signal for both the generator and the discriminator, resulting in a stable training dynamic. We apply our training method to pre-trained language models, using data from their original training set but less than 0.01% of the available data. A comprehensive human evaluation shows that our method significantly improves the quality of texts generated by the model while avoiding the previously reported sparsity problems of GAN approaches. Even our smaller models outperform larger original baseline models with more than 16 times the number of parameters. Finally, we corroborate previous claims that perplexity on held-out data is not a sufficient metric for measuring the quality of generated texts.