The noise-to-image sampling process

Here are the steps to sample an image from the model, or, in other words, generate an image from the reverse diffusion process:

1. Generate a complete Gaussian noise with a mean of 0 and a variance of 1:

x T ∼ 𝒩(0,1)

We will use this noise as the starting image.

2. Loop through t = T to t = 1. In each step, if t > 1, then generate another Gaussian noise image z:

z ∼ 𝒩(0,1)

If t = 1, then the following occurs:

z = 0

Then, generate a noise from the UNet model, and remove the generated noise from the input noisy image x t:

x t-1 =  1 _ √ _ α t (x t −  1 − α t _ √ _ 1 − _ α t  ϵ θ(x t, t)) + √ _ 1 − α t  z

If we take a look at the preceding equation, all those α&...