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

• URL: http://arxiv.org/abs/2410.04479v2
• Date: Mon, 26 May 2025 17:20:09 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.<n>We state three conditions for achieving measurement-consistent diffusion trajectories.<n>We propose a new optimization-based sampling method that not only enforces standard data manifold measurement consistency and forward diffusion consistency, but also incorporates our proposed step-wise and network-regularized backward diffusion consistency.
• 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 problems, the reverse sampling steps are modified to approximately sample from a measurement-conditioned distribution. However, these modifications may be unsuitable for certain settings (e.g., presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier 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 standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates our proposed step-wise and network-regularized 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 (implicitly or explicitly), our sampler requires significantly fewer reverse steps. Therefore, we refer to our method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to SOTA baselines, our experiments across several linear and non-linear tasks (with natural and medical images) demonstrate that SITCOM achieves competitive or superior results in terms of standard similarity metrics and run-time.

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