The recent advancements in diffusion models have significantly pushed the boundaries of generative modeling, particularly in areas such as image generation, discrete data control, and progressive coding. A notable trend is the development of more efficient sampling techniques, such as analytical teleportation and optimized few-step samplers, which aim to reduce computational costs without compromising sample quality. Additionally, there is a growing interest in integrating diffusion models with compression techniques, leading to novel approaches like universally quantized diffusion models that offer competitive rate-distortion performance. Discrete diffusion models are also gaining traction, with innovative guidance mechanisms that enhance control over discrete data generation. Distributed estimation methods are being refined to handle quantized measurements and communication over dynamic topologies, showcasing advancements in stochastic approximation and consensus-based algorithms. Theoretical bounds, such as Wasserstein distance estimates for generative models, are providing deeper insights into the convergence and complexity of these models. Overall, the field is moving towards more efficient, controllable, and theoretically grounded generative modeling solutions.