Diffusion Models
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
Resources
- Google AI Blog High Fidelity Image Generation Using Diffusion Models - discusses SR3 and CDM