SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems

• URL: http://arxiv.org/abs/2410.04479v1
• Date: Sun, 6 Oct 2024 13:39:36 GMT
• Title: SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems
• Authors: Ismail Alkhouri, Shijun Liang, Cheng-Han Huang, Jimmy Dai, Qing Qu, Saiprasad Ravishankar, Rongrong Wang,
• Abstract summary: Diffusion models (DMs) are a class of generative models that allow sampling from a distribution learned over a training set. DMs are typically modified to approximately sample from a measurement-conditioned distribution in the image space. These modifications may be unsuitable for certain settings (such as in the presence of measurement noise) and non-linear tasks. We state three conditions for achieving measurement-consistent diffusion trajectories.
• Score: 14.2814208019426
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion models (DMs) are a class of generative models that allow sampling from a distribution learned over a training set. When applied to solving inverse imaging problems (IPs), the reverse sampling steps of DMs are typically modified to approximately sample from a measurement-conditioned distribution in the image space. However, these modifications may be unsuitable for certain settings (such as in the presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier sampling steps and generally require a large number of optimization and/or sampling steps. To address these challenges, we state three conditions for achieving measurement-consistent diffusion trajectories. Building on these conditions, we propose a new optimization-based sampling method that not only enforces the standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates backward diffusion consistency that maintains a diffusion trajectory by optimizing over the input of the pre-trained model at every sampling step. By enforcing these conditions, either implicitly or explicitly, our sampler requires significantly fewer reverse steps. Therefore, we refer to our accelerated method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to existing state-of-the-art baseline methods, under different levels of measurement noise, our extensive experiments across five linear and three non-linear image restoration tasks demonstrate that SITCOM achieves competitive or superior results in terms of standard image similarity metrics while requiring a significantly reduced run-time across all considered tasks.

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