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

• URL: http://arxiv.org/abs/2307.00619v1
• Date: Sun, 2 Jul 2023 17:21:30 GMT
• Title: Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
• Authors: Litu Rout and Negin Raoof and Giannis Daras and Constantine Caramanis and Alexandros G. Dimakis and Sanjay Shakkottai
• Abstract summary: We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting.
• Score: 98.95988351420334
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to 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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