Recently, diffusion models, with their powerful generative capabilities, have become one of the hot topics in generative models. Application areas include computer vision, speech generation, bioinformatics, and natural language processing. Diffusion probabilistic models were initially proposed as latent variable generative models inspired by non-equilibrium thermodynamics. These models consist of two processes: the forward process, which adds noise at multiple scales, gradually disturbing the data distribution; and the reverse process, which learns to recover the data structure. This chapter covers the theory and application of diffusion models. Section 16.1 discusses fraction-based generative networks with Langevin dynamics; Sect. 16.2 introduces denoising diffusion probabilistic models; Sect. 16.3 analyzes denoising diffusion implicit models (DDIMs); Sect. 16.4 discusses the SDE framework that encapsulates previous methods; Sect. 16.5 introduces the application of diffusion models in image and video synthesis; Sect. 16.6 discusses another application, image-to-image translation; Sect. 16.7 introduces the application of diffusion models in text-to-image/video generation; Sect. 16.8 introduces the application of diffusion models in policy and planning learning, Sect. 16.9 summarizes some improvements to diffusion models.