Diffusion models have shown remarkable capabilities in generating high-fidelity data across modalities such as images, audio, and video. However, their computational intensity makes deployment on edge devices a significant challenge. This survey explores the foundational concepts of diffusion models, identifies key constraints of edge platforms, and synthesizes recent advancements in model compression, sampling efficiency, and hardware-software co-design to make diffusion models viable on edge devices. We also review promising applications and suggest future research directions.