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Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models

Litu Rout · Negin Raoof · Giannis Daras · Constantine Caramanis · Alex Dimakis · Sanjay Shakkottai

Great Hall & Hall B1+B2 (level 1) #913
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[ Paper [ Slides [ Poster [ OpenReview
Wed 13 Dec 3 p.m. PST — 5 p.m. PST


We present the first framework to solve linear inverse problems leveraging pre-trained \textit{latent} diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to \textit{pixel-space} diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

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