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How is the variance for a diffusion kernel derived for a diffusion model?

So I'm watching this video tutorial from CVPR this year on diffusion models, and I am confused by the variance term in the distribution on the left on the video. … .$$ If we define $\bar{\alpha} = \prod_{s = 1}^t(1 - \beta_t),$ then we are supposed to derive the diffusion kernel $$q(\mathbf{x}_t|\mathbf{x}_{0}) = N(\mathbf{x}_t;\sqrt{\bar{\alpha}}\mathbf{x}_0,(1 …
Cynthia Kim's user avatar