Maximum Consensus Framework for Robust Diffusion Posterior Sampling in Noisy Inverse Problems

초록

Existing diffusion-based approaches for inverse problems typically leverage Bayes' rule to connect pretrained diffusion models with measurement-fitting approximations. These methods aim to jointly satisfy manifold feasibility and measurement-structure consistency during the reverse diffusion process. However, these approaches can lead to deviations from the data manifold due to the measurement inconsistency, particularly under outlier corruption, which distorts the data distribution toward high-entropy regions beyond typical noise levels. To tackle these challenges, we propose a diffusion-based posterior sampling method using the Maximum Consensus Framework (DMCF). DMCF leverages MCF-based guidance for the pretrained diffusion model, iteratively suppressing the influence of noise and outliers by maximizing the number of samples that conform to consensus patterns aligned with the underlying structure. Extensive experimental evaluations on both linear and non-linear inverse problems, encompassing diverse image restoration tasks such as inpainting, deblurring, super-resolution, and phase retrieval, provide robust evidence the efficacy of the proposed method. The results demonstrate that the proposed method consistently outperforms state-of-the-art diffusion-based sampling approaches, achieving gains of up to 3.3% in PSNR and 4.1% in SSIM, with particularly strong performance in the presence of significant outliers.

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