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.

翻译：扩散模型已被证明是信号恢复的强大先验，但其在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。这一困难源于这些任务中固有的非线性链接函数，该函数要么不可微，要么缺乏显式表征。为解决此问题，我们提出了Diff-OneBit，这是一种快速有效的基于扩散模型的1比特量化信号恢复方法。Diff-OneBit通过利用可微的代理似然函数对1比特量化进行建模，从而支持基于梯度的迭代，以应对不可微或隐式链接函数带来的挑战。该函数被集成到一个灵活的即插即用框架中，将数据保真项与扩散先验解耦，允许任何预训练的扩散模型在迭代重建过程中充当去噪器。在FFHQ、CelebA和ImageNet数据集上的大量实验表明，Diff-OneBit能够生成高保真重建图像，在1比特压缩感知和逻辑回归任务中，其重建质量和计算效率均优于现有最先进方法。