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.

Diffusion models (DMs) have demonstrated remarkable ability to generate diverse and high-quality images by efficiently modeling complex data distributions. They have also been explored as powerful generative priors for signal recovery, resulting in a substantial improvement in the quality of reconstructed signals. However, existing research on signal recovery with diffusion models either focuses on specific reconstruction problems or is unable to handle nonlinear measurement models with discontinuous or unknown link functions. In this work, we focus on using DMs to achieve accurate recovery from semi-parametric single index models, which encompass a variety of popular nonlinear models that may have {\em discontinuous} and {\em unknown} link functions. We propose an efficient reconstruction method that only requires one round of unconditional sampling and (partial) inversion of DMs. Theoretical analysis on the effectiveness of the proposed methods has been established under appropriate conditions. We perform numerical experiments on image datasets for different nonlinear measurement models. We observe that compared to competing methods, our approach can yield more accurate reconstructions while utilizing significantly fewer neural function evaluations.

Recorded seismic signals are of fundamental importance in earthquake engineering, serving as vital data for analyzing and comprehending various ground motion parameters that are crucial for seismic design. However, ground motions usually suffer from noise contamination, resulting in baseline drift. The drift can introduce significant biases in ground motion parameters, especially those associated with displacement time histories. To address the aforementioned issues, this paper proposes a seismic signal denoising generative adversarial network (SDGAN), which is a conditional Wasserstein GAN composed of a generator and a discriminator. SDGAN is trained on a database constructed from the STanford EArthquake Dataset (STEAD) and the INSTANCE dataset. We compared the trained model with the Butterworth filter, a spectral filtering-based method, and DeepDenoiser, a deep learning-based denoising method. The results demonstrate the SDGAN’s efficacy in the simultaneous removal of various types of noise and baseline drift with minimal information loss, even in scenarios characterized by significantly low signal-to-noise ratio (SNR). Moreover, we substantiate the exceptional generalization performance of SDGAN using the real noisy seismic signals recorded in Kyoshin Network (K-Net).