Diffusion Models: Difference between revisions
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==Image Generation== | ==Image Generation== | ||
===DDPM=== | |||
See [https://arxiv.org/pdf/2006.11239.pdf DDPM paper]<br> | |||
Here, the diffusion process is modeled as: | |||
* Forward: <math>q(\mathbf{x}_t, \mathbf{x}_{t-1}) \sim N(\sqrt{1-\beta_t} \mathbf{x}_{t-1}, \beta_t \mathbf{I})</math> | |||
* Reverse: <math>p_\theta(\mathbf{x}_{t-1}, \mathbf{t}) \sim N( \mu_\theta (x_t, t), \beta_t \mathbf{I})</math> | |||
The forward diffusion can be sampled for any <math>t</math> using:<br> | |||
<math>\mathbf{x}_{t} = \sqrt{\bar\alpha_t} \mathbf{x}_0 - \sqrt{1-\bar\alpha_t} \boldsymbol{\epsilon}</math> where <math>\bar\alpha_t = \prod_{s=1}^{t}(1-\beta{s})</math> | |||
===Super-resolution=== | ===Super-resolution=== | ||
See [https://iterative-refinement.github.io/ SR3 iterative refinement] | See [https://iterative-refinement.github.io/ SR3 iterative refinement] | ||