Understanding the image-to-noise process
The idea of the diffusion model is inspired by the diffusion concept from thermodynamics. Take one image as a cup of water and add enough noise (ink) to the image (water) to finally turn the image (water) into a complete noise image (ink water).
As shown in Figure 4.1, image x 0 can be converted to a nearly Gaussian (normally distributed) noise image x T.
Figure 4.1: Forward diffusion and reverse denoising
We employ a predetermined forward diffusion process, denoted as q, which systematically introduces Gaussian noise to an image until it culminates in pure noise. The process is denoted by q(x t | x t-1). Note that the reverse process p θ(x t-1 | x t) is still unknown.
One step of the forward diffusion process can be denoted as follows:
q(x t | x t-1) ≔ 𝒩(x t; √ _ 1 − β t x t-1 , β...
