Method Issue

[studying910]

According to the multi-step DDIM sampling, it is mentioned in Section 3.2 that Eqn. (13) is derived from Eqn. (11).

However, it is quite confused since Eqn. (11) seems incorrect.

The DDIM sampling seems to be:

$\frac{\tilde{x}_s}{\sqrt{\overline{\alpha}_s}}=\frac{x_t}{\sqrt{\overline{\alpha}_t}}+(\gamma(s)-\gamma(t)) \epsilon(x_t; y, \phi)$.

Since $\overline{\alpha}_0=1$, it can derive Eqn. (13).

Also, the notation of the sampling latents $\tilde{x}_s \dots$ is missed.

[AbnerVictor]

Thank you for asking. We will check your problem ASAP

[AbnerVictor]

Thank you for asking, your induction is correct.

our original intention of Eqn.11 is to express the ddim denoising process in a similar way of Eqn.9, which is the ddim inversion. We make a mistake in the writing, we will fix that ASAP.

[studying910]

Thx for your answer :)

[AbnerVictor]

Thx for your answer :)

Thank you for pointing out the problem. The revised Eqn.11 should be: $\tilde{x} _{t-\deltaT} = \sqrt{\bar \alpha {t-\delta_T}}(\hat{x}_0^t + \gamma(t-\deltaT)\epsilon \phi(x_t, t, y))$.

Where $\hat{x}_0^t = \frac{1}{\sqrt{\bar \alpha _t}}xt - \gamma (t) \epsilon \phi(x_t, t, y)$