Continuous Diffusion Language Models (CDLMs) represent a generative paradigm that applies continuous corruption processes, such as Gaussian noise, to discrete categorical data by "lifting" the process into a continuous embedding space. Unlike discrete diffusion models (DDLMs) or autoregressive models, CDLMs manipulate real-valued vectors to model token sequences. Key technical components include embedding strategies—ranging from one-hot representations and pre-trained BERT embeddings to jointly learned embeddings—and specific loss functions like Mean Squared Error (MSE) or cross-entropy (often via score interpolation). A critical challenge in CDLMs is the noise schedule; because meaningful corruption occurs within a narrow range of noise levels in high-dimensional embedding spaces, researchers use adaptive schedules, such as those employing entropy linearization, to focus modeling capacity on informative noise levels. Additionally, self-conditioning—passing the denoiser's previous prediction as an auxiliary input—has proven essential for boosting sample quality. Despite these advancements, the field faced a "continuous extinction" after 2023, largely due to the massive training efficiency gap; for instance, the Plaid-1B model was found to be 64x less efficient than autoregressive baselines. Current research interest is shifting back toward these methods as the community seeks alternatives to the sequential nature of autoregression.