Diffusion Model Based Signal Recovery Under 1-Bit Quantization

2025-11-16

AI Summary

In 1-bit quantized signal recovery, the non-differentiability and implicit nature of the nonlinear link function hinder the integration of diffusion models (DMs). To address this, we propose Diff-OneBit: a plug-and-play (PnP) framework leveraging a differentiable surrogate likelihood function. Our method reformulates the nonsmooth or implicit data-fidelity term as a differentiable approximation, decoupling the observation model from the pre-trained DM prior and enabling arbitrary DMs as denoisers. Evaluated on 1-bit compressive sensing and logistic regression tasks, Diff-OneBit significantly improves reconstruction fidelity and convergence speed. Experiments on FFHQ, CelebA, and ImageNet demonstrate state-of-the-art performance in PSNR, SSIM, and inference efficiency—achieving both high accuracy and practical deployability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Addressing non-differentiable link functions in 1-bit quantization
• Enabling gradient-based signal recovery with surrogate likelihood modeling
• Improving reconstruction quality and efficiency in 1-bit compressed sensing

Innovation

• Differentiable surrogate likelihood models 1-bit quantization
• Plug-and-play framework decouples data fidelity from diffusion prior
• Pretrained diffusion models act as denoisers in iterative reconstruction