Diffusion Models

From David's Wiki
\( \newcommand{\P}[]{\unicode{xB6}} \newcommand{\AA}[]{\unicode{x212B}} \newcommand{\empty}[]{\emptyset} \newcommand{\O}[]{\emptyset} \newcommand{\Alpha}[]{Α} \newcommand{\Beta}[]{Β} \newcommand{\Epsilon}[]{Ε} \newcommand{\Iota}[]{Ι} \newcommand{\Kappa}[]{Κ} \newcommand{\Rho}[]{Ρ} \newcommand{\Tau}[]{Τ} \newcommand{\Zeta}[]{Ζ} \newcommand{\Mu}[]{\unicode{x039C}} \newcommand{\Chi}[]{Χ} \newcommand{\Eta}[]{\unicode{x0397}} \newcommand{\Nu}[]{\unicode{x039D}} \newcommand{\Omicron}[]{\unicode{x039F}} \DeclareMathOperator{\sgn}{sgn} \def\oiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x222F}\,}{\unicode{x222F}}{\unicode{x222F}}{\unicode{x222F}}}\,}\nolimits} \def\oiiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x2230}\,}{\unicode{x2230}}{\unicode{x2230}}{\unicode{x2230}}}\,}\nolimits} \)

Background

By Sohl-Dickstein et al.[1].

The goal is to define a mapping between a complex distribution \(\displaystyle q(\mathbf{x}^{(0)})\) (e.g. set of realistic images) to a simple distribution \(\displaystyle \pi(\mathbf{y})=p(\mathbf{x}^{(T)})\)(e.g. multivariate normal).
This is done by defining a forward trajectory \(\displaystyle q(\mathbf{x}^{(0...T)})\) and optimizing a reverse trajectory \(\displaystyle p(\mathbf{x}^{(0 ... T)})\).
The forward trajectory is repeatedly applying a Markov diffusion kernel (i.e. a function with a steady distribution \(\displaystyle \pi(\mathbf{y})\)), performing T steps of diffusion.
The reverse trajectory is again applying a diffusion kernel but with an estimated mean and variance.

Image Generation

Super-resolution

See SR3 iterative refinement

Resources