While diffusion models excel at conditionally generating high-quality images, prior works in discrete diffusion models were not evaluated on conditional long-text generation. This work addresses the limitations of prior discrete diffusion models for conditional long-text generation, particularly in the long abstractive summarization task. Despite faster decoding speeds compared to autoregressive methods, previous discrete diffusion models failed on the abstractive summarization task due to the incompatibility between the backbone architectures and the random noising process. To overcome these challenges, we introduce a novel semantic-aware noising process that enables Transformer backbones to handle long sequences effectively. Additionally, we propose CrossMamba, an adaptation of the Mamba model to the encoder-decoder paradigm, which integrates seamlessly with the random absorbing noising process. Our approaches outperform existing discrete diffusion models on three benchmark summarization datasets: Gigaword, CNN/DailyMail, and Arxiv, while also achieving much faster inference speed compared to autoregressive models.