Introduction

A diffusion probabilistic model (which we will call a “diffusion model” for brevity) is a parameterized Markov chain trained using variational inference to produce samples matching the data after finite time.

… learned to reverse a diffusion process,$q(\mathrm{x}t|\mathrm{x}{t-1})$ which is a Markov chain that gradually adds noise to the data in the opposite direction of sampling until signal is destroyed.

When the diffusion consists of small amounts of Gaussian noise, it is sufficient to set the sampling chain transitions to conditional Gaussians too, allowing for a particularly simple neural network parameterization.

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Background

처음 diffusion에서 제시된 개념중 중요한 것은

Noise가 추가되는 과정 : forward trajectory(diffusion process)
Denoising : reverse process
이 때 Gaussian Markov process가정
(diffusion rate $\beta_t$가 작다면) 두 process는 동일한 distribution을 가지게 된다.

Forward Process

Initial and Final State

초기 값은 WLOG, 시작점을 기존의 데이터에서 하나 sampling해서 가져온다고 생각하자!