Question about the equation of deterministic DDIM sampling in the Null-text Inversion paper

[wendy-xiaozong]

Hi,

Thanks for this wonderful work! I have a question about the equation of deterministic DDIM sampling in the Null-text Inversion paper.

Based on my understanding, deterministic DDIM sampling is to set the $\sigma_t=0$ for equation 12 in the DDIM paper. It should be the following equation:
$z_{t-1} = \sqrt{\alpha_{t-1}}\left(\frac{z_t - \sqrt{1-\alpha_t}\cdot\epsilon_\theta(z_t,\mathcal{C},t)}{\sqrt{\alpha_t}}\right) + \sqrt{1-\alpha_{t-1}}\cdot\epsilon_\theta(z_t, \mathcal{C}, t)$
If you rewrite this equation into the Null-text Inversion paper version, it should be:
$z_{t-1} = \sqrt{\frac{\alpha_{t-1}}{\alpha_t}}z_t + \sqrt{\alpha_{t-1}}\left(\sqrt{\frac{1}{\alpha_{t-1}} - 1}- \sqrt{\frac{1}{\alpha_t}-1} \right)\cdot\epsilon_\theta(z_t, \mathcal{C}, t)$
Which is different from it the Null-text Inversion paper.

It may be my understanding is wrong. I would very much appreciate it if you could point me in the right direction!

Thanks,

Jueqi

[junseokoh1]

I have the sam question. When I campare equation of deterministic DDIM sampling in the Null-text Inversion paper, it is different with DDIM & DiffuisonCLIP & Diffusion models beat GAN papers.

[jwh97nn]

same question here, thought it would be a typo

[YasminZhang]

It is a typo!