Diffusion Model Based Signal Recovery Under 1-Bit Quantization

TL;DR

This paper introduces Diff-OneBit, a diffusion model-based method that effectively recovers signals from 1-bit quantized data by using a surrogate likelihood function, enabling high-quality image reconstruction in various tasks.

Contribution

The paper proposes Diff-OneBit, a novel diffusion model framework that handles non-differentiable 1-bit quantization functions via surrogate likelihoods, improving reconstruction quality and efficiency.

Findings

Outperforms state-of-the-art methods in image reconstruction quality

Achieves higher computational efficiency in 1-bit signal recovery

Demonstrates effectiveness across multiple datasets and tasks

Abstract

Diffusion models (DMs) have demonstrated to be powerful priors for signal recovery, but their application to 1-bit quantization tasks, such as 1-bit compressed sensing and logistic regression, remains a challenge. This difficulty stems from the inherent non-linear link function in these tasks, which is either non-differentiable or lacks an explicit characterization. To tackle this issue, we introduce Diff-OneBit, which is a fast and effective DM-based approach for signal recovery under 1-bit quantization. Diff-OneBit addresses the challenge posed by non-differentiable or implicit links functions via leveraging a differentiable surrogate likelihood function to model 1-bit quantization, thereby enabling gradient based iterations. This function is integrated into a flexible plug-and-play framework that decouples the data-fidelity term from the diffusion prior, allowing any pretrained DM to act as a denoiser within the iterative reconstruction process. Extensive experiments on the FFHQ, CelebA and ImageNet datasets demonstrate that Diff-OneBit gives high-fidelity reconstructed images, outperforming state-of-the-art methods in both reconstruction quality and computational efficiency across 1-bit compressed sensing and logistic regression tasks. Our code is available at https://github.com/Chenyouming123/DiffOneBit.