diff --git a/docs/index.md b/docs/index.md index e6d981d..79cf0bf 100644 --- a/docs/index.md +++ b/docs/index.md @@ -114,15 +114,16 @@ $$ $\mathbb{E}[\epsilon_t | z_t]$ is the quantitiy that eps-prediction models try to estimate, with $$ -\hat{\epsilon}_\theta(z_t, \sigma_t) \approx \mathbb{E}[\epsilon_t | z_t] +\hat{\epsilon}_{\theta}(z_t, \sigma_t) \approx \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 $\theta$. +where +$\hat{\epsilon}_{\theta}(z_t, \sigma_t)$ 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 $z_t - \sigma_t \hat{\epsilon}_\theta(z_t, \sigma_t)$. +However this rescaling is not necessary and is not done in the ComfyUI implementation, there the "denoised output" is simply +$z_t - \sigma_t \hat{\epsilon}_{\theta}(z_t, \sigma_t)$. TODO CHECK WHETHER THE RESCALING HAPPENS SOMEWHERE ELSE IN THE SAMPLER OR BEFORE THE VAE DECODING