Diffusion Models for Inverse Problems

Hyungjin Chung presents his papers:
"Diffusion posterior sampling for general noisy inverse problems" arxiv.org/pdf/2209.14687.pdf
"Improving diffusion models for inverse problems using manifold constraints"
arxiv.org/pdf/2206.00941.pdf

[@edvinbeqari7551]

On the minus sign comment, the confusion arises from the fact that we call this a reverse diffusion process. Its not - its conditioned on the highest probability of the distribution function or any transformation of it. If you you were to plot the two diffusions (forward and conditional), they look completely different. Anyways, minus sign because the gradient will reverse your sign to keep you on the highest probability ridge.

[@akhilpremk]

dt is negative in the reverse SDE and positive in the forward SDE. See paragraph under (6) of arXiv:2011.13456v2. Intuitively, we can understand the sign by taking g(t) to 0. Then the evolution is deterministic, and governed only by the drift force f(x,t) in the forward direction. Since this process is Markovian, the reverse process is simply dx = -f(x,t) |dt|.

[@MilesBellas]

I wish the audio had been processed to eliminate the compression aberrations.

[@maerlich]

Excellent talk. Very enlightening! ❤

[@user-xc4jk6vn2h]

I have one question: Why is it that we can factorize as shown at 12:44 given that x_0 is independent on y and x_t?

[@chenningyu]

great talk, thanks for sharing! (LHS in slides 18-21 should be p(y|x_t))

[@RoboticusMusic]

I think I missed the high level, what is the SoTA technology here, what applications? Mostly for reversing complicated smudges and blurring? Other applications?