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Diffusion models are multi-step iterative sampling models designed to transition from noise to images along the trajectory of a Probability Flow Ordinary Differential Equation (PF ODE). That is, during the temporal step shift from \([T, ..., 0]\), the images predicted by the diffusion model evolve from a standard Gaussian noise distribution to a clean image distribution. The distributions in the intermediate process lie between Gaussian noise and the image distribution. However, multi-step iterative sampling requires substantial computational resources, which is not conducive to the application of diffusion models....

The one-step noise reduction sampling of a student diffusion model that approximates the two- or four-step noise reduction sampling of a teacher model is referred to as progressive distillation. The sampling steps of the student model decrease in the sequence from 128 to 32, then to 8, 4, 2, and finally to 1. Jo, in 2022, introduced Progressive Distillation (PD), marking the inaugural work to propose the ideology of progressive distillation....

The content introduced in this article pertains to SMLD, NCSN, DDPM, and SDEs. Before we proceed with the main body of the article, I will first clarify the specific relationships among these concepts for the readers. The SMLD model, proposed by Dr. Song in his 2019 thesis, is a generative method primarily composed of score matching and Langevin dynamics sampling. Given that this method has certain limitations—details of which are presented in the mathematical reasoning section—the author introduced the NCSN method as an improvement....

Diffusion Models (DM) have achieved remarkable progress in the realms of image, video, and audio processing. This paper delves into the foundational work of the diffusion models, namely the Denoise Diffusion Probability Model (DDPM), and further introduces the widely used rapid sampling technique within diffusion models, the Denoise Diffusion Implicit Model (DDIM). The focus of this paper is on the modeling principles, training processes, and inference methods of DDPM and DDIM....