Popularized by their remarkable image generation performance, diffusion and related methods for mass transport (“diffusion” for short) have found widespread success across visual media applications. This talk will examine the recent impact of diffusion modeling on lossy data compression, where diffusion-based generative compression methods can now produce photorealistic reconstructions at extremely low bitrates. While most existing methods follow a common algorithmic framework that employs conditional diffusion for decoding, recent work has also begun to explore the use of diffusion models themselves for information transmission. Along the way we will discuss connections to inverse problem solving and rate-distortion-realism theory, examine architectural choices, and identify open research questions.