Diffusing the mathematical equations of Diffusion Modelling
Over the past two years, the body of research on diffusion models has grown significantly. In this blog, I explain the foundations of diffusion models.
Denoising Diffusion probabilistic model has two steps in it:-
- Forward Diffusion: Add gaussian noise at each step to the input
- Reverse Diffusion: Approximate the denoised input at each step
Forward Diffusion
At every step we assume to generate noisy image conditioned on previous image using a normal distribution. This normal distribution, takes the image at previous step, rescales it by a factor of sqrt(1 — β_t) and adds tiny bit of noise with a variance of β_t. The schedule of β’s is defined such that β1<β2<β3<…<β_T, where T is the last step in forward iteration.
We can also define the joint distribution for all the samples that will be generated in this chain of forward diffusion starting from x1 till xT as
But since we are using such a simple distribution to generate samples in forward diffusion, cant we just jump to any t step in the forward chain using function…
