Diffusion Models: Difference between revisions
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==Background== | ==Background== | ||
By Sohl-Dickstein ''et al.''[https://arxiv.org/pdf/1503.03585.pdf]. | |||
The goal is to define a mapping between a complex distribution <math>q(\mathbf{x}^{(0)})</math> (e.g. set of realistic images) to a simple distribution <math>\pi(\mathbf{y})=p(\mathbf{x}^{(T)})</math>(e.g. multivariate normal).<br> | |||
This is done by defining a forward trajectory <math>q(\mathbf{x}^{(0...T)})</math> and optimizing a reverse trajectory <math>p(\mathbf{x}^{(0 ... T)})</math>.<br> | |||
The forward trajectory is repeatedly applying a Markov diffusion kernel (i.e. a function with a steady distribution <math>\pi(\mathbf{y})</math>), performing T steps of diffusion.<br> | |||
The reverse trajectory is again applying a diffusion kernel but with an estimated mean and variance.<br> | |||
==Image Generation== | ==Image Generation== | ||