whole reverse process as a function R

[jiayangshi]

Hi, thanks for the great work and providing code.

I have a question regarding the function R.

1: Apparently this is the important contribution of the paper and it is claimed to assure feasibility on the manifold as shown in Figure 3. Also it is claimed that " viewing the whole reverse process as a function R ". In the Figure 3 it appears that you map each intermediate latent noise through R to the target image and promote data consistency with y-A(R(z)). There I have difficulty to understand the essential difference of the proposed method compared with DPS combined with latent diffusion model or PLSD, where they(PLSD) also do data consistency step based on the \hat{x_0} estimate of each step. I wonder if I have understood your method correctly?

2: Although in Figure 3 and in text you state that " viewing the whole reverse process as a function R ", and do data consistency step there. In your code, you don't really apply R to the intermediate latent variable, but rather compute the data consistency step based on the latent variable of previous step. I wonder is there any specific reason for that?

Thank you in advance!