diff --git a/docs/index.md b/docs/index.md index 631b642..64409d4 100644 --- a/docs/index.md +++ b/docs/index.md @@ -111,9 +111,9 @@ $$ \mathbb{E}[x|z_t] = \frac{z_t - \sigma_t \mathbb{E}[\epsilon_t | z_t] }{\alpha_t} $$ -- $\mathbb{E}[\epsilon_t | z_t]$ is the quantitiy that eps-prediction models try to estimate, with $\hat{\epsilon}_\theta(z_t, \sigma_t) \sim \mathbb{E}[\epsilon_t | z_t]$. -- $\hat{\epsilon}_\theta(z_t, \sigma_t)$ is the model's noise prediction for the current time step, using fitted neural network parameters $\theta$. -- $\mathbb{E}[x|z_t]$ is the denoised output or prediction of the diffusion model at time $t$. +$\mathbb{E}[\epsilon_t | z_t]$ is the quantitiy that eps-prediction models try to estimate, with $\hat{\epsilon}_\theta(z_t, \sigma_t) \sim \mathbb{E}[\epsilon_t | z_t]$.\ +$\hat{\epsilon}_\theta(z_t, \sigma_t)$ is the model's noise prediction for the current time step, using fitted neural network parameters $\theta$.\ +$\mathbb{E}[x|z_t]$ is the denoised output or prediction of the diffusion model at time $t$.\ Note that the divison by $\alpha_t$ is a problem at the last step, since $\alpha_T$ is very small, or even zero for ZSNR models. \ However this rescaling is not necessary and is not done in the ComfyUI implementation, there the "denoised output" is simply $z_t - \sigma_t \hat{\epsilon}_\theta(z_t, \sigma_t)$.