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DPS2022 / diffusion-posterior-sampling

Official pytorch repository for "Diffusion Posterior Sampling for General Noisy Inverse Problems"
https://dps2022.github.io/diffusion-posterior-sampling-page/
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Formulation for Gaussian Sampling #16

Closed MichaelJacob914 closed 3 months ago

MichaelJacob914 commented 3 months ago

In the paper, if I understand x'_{t-1} is the standard sampling method before using the posterior sampling method,

Screenshot 2024-07-26 at 4 32 01 PM

but in standard DDIM/DDPM sampling, x_{t-1} is given as

Screenshot 2024-07-26 at 4 32 37 PM

Is there anywhere in the paper explaining where the former is derived from the standard equation?

MichaelJacob914 commented 3 months ago

I found the derivation, just need to relate DDIM to DDPM and then when you plug in $\hat{x}_{0}$ into equation 6, it simplifies greatly as was the case in the original DDPM paper.