Explore the emergence and evolution of diffusion models, a powerful class of generative AI models that learn to synthesize data by reversing a gradual noising process. Initially successful in image and audio generation, researchers are increasingly adapting them to Natural Language Processing (NLP), giving rise to diffusion-based Large Language Models (LLMs).

The text details the theoretical foundations rooted in non-equilibrium thermodynamics and Stochastic Differential Equations (SDEs), highlights landmark developments like DDPMs and Score-Based Generative Modeling, and compares them to traditional models like GANs and VAEs. Key challenges in applying diffusion models to the discrete nature of text are discussed, along with innovative architectural blueprints and training methodologies for diffusion LLMs, including various masking strategies, noise scheduling, and loss functions.

The sources also cover the practical applications in NLP (text generation, code generation, machine translation), image generation, and audio synthesis, while acknowledging significant limitations related to computational efficiency and scalability, pointing towards exciting future research directions.