In this post, I will introduce perturbation kernels in diffusion models.
Before reading this post, I recommend reading my previous posts.
- Reverse SDE in diffusion models
- Denoising score matching loss in diffusion models
- Score model in diffusion models
- Score function of a stochastic process
Forward stochastic differential equation (SDE)
Forward SDE describes a process where a data sample x_0 is corrupted into a gaussian noise
dx_t = f(x_t, t) dt + g(t) dw_t. \tags{Forward SDE}The stochastic process x_t governed is by the (Forward SDE).
Perturubation Kernel
Let x_t be the stochastic process goverend by (Forward SDE). Consider a conditional probability density function (pfd) p_{0t} (x_t \mid x_0) of x_t given x_0 . In diffusion models, the conditional pdf is called the perturbation kernel.