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Fix DDPM covariance notation and noise-scale prose in unit 1 - #120
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Match q(x_t | x_0) in notebook 02 to notebook 01 by using covariance (1 - bar-alpha_t) I instead of a square-root on the covariance, and describe the forward step as adding noise scaled by sqrt(beta_t). Co-authored-by: Charles <CharlesXmf@users.noreply.github.com>
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Fixes #63
The closed-form$q(x_t \mid x_0)$ in $\mathcal{N}(\mu, \Sigma)$ , writing $\sqrt{(1-\bar\alpha_t)}\mathbf{I}$ instead of the covariance $(1-\bar\alpha_t)\mathbf{I}$ . Notebook 01 already had the covariance form.
unit1/02_diffusion_models_from_scratch.ipynbused a standard-deviation scaling insideIn the same cells, the stepwise process is$q(x_t \mid x_{t-1}) = \mathcal{N}(x_t; \sqrt{1-\beta_t}x_{t-1}, \beta_t I)$ , so the equivalent sample adds noise scaled by $\sqrt{\beta_t}$ , not $\beta_t$ . That prose is updated in both notebook 01 and 02.
Plot labels such as
sqrt_one_minus_alpha_prodare left unchanged, since those refer to the implementation's std-dev scale.