An introduction to diffusion language models and the research advances that underlie today's diffusion LLMs. We describe the building blocks of recent open-source models, starting from simple masking diffusion, and including techniques for iterative refinement, post-training, and variable-length generation. Material is adapted from workshop talks and lectures at ICLR 2026 and MLSS 2026. Two families of generative AI algorithms are widely used today. For continuous data such as images or video, the state-of-the-art approach is based on diffusion models. For discrete data such as text or code, t