用可微代理似然函数解决1比特量化信号恢复难题
Diffusion Model Based Signal Recovery Under 1-Bit Quantization
- 设计可微代理似然函数处理非可导的1比特映射
- 在FFHQ/CelebA/ImageNet上重建质量超越现有方法
- 适配任意预训练扩散模型，支持快速迭代恢复
扩散模型（DMs）在信号恢复中表现出强大先验能力，但在1比特量化任务（如1比特压缩感知和逻辑回归）中的应用仍面临挑战，主要源于任务中固有的非线性链接函数——这些函数要么不可导，要么缺乏显式表达。为此，本文提出Diff-OneBit，一种基于扩散模型的高效1比特量化信号恢复方法。该方法通过引入可微代理似然函数建模1比特量化过程，使梯度迭代成为可能。该函数被嵌入一个灵活的即插即用框架，将数据保真项与扩散先验解耦，允许任意预训练扩散模型作为去噪器参与迭代重建。在FFHQ、CelebA和ImageNet数据集上的大量实验表明，Diff-OneBit在1比特压缩感知和逻辑回归任务中均实现高保真图像重建，其重建质量与计算效率均优于当前最优方法。
原文摘要 · Abstract (English)
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.
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