Diffusion Model Based Signal Recovery Under 1-Bit Quantization

TL;DR

This work tackles signal recovery under 1-bit quantization by marrying diffusion-model priors with a differentiable surrogate likelihood for 1-bit measurements. Diff-OneBit adopts a plug-and-play, half-quadratic splitting strategy to decouple the data-fidelity term from the diffusion prior, enabling gradient-based updates and Tweedie-based denoising within the reverse diffusion process. Across 1-bit CS and logistic regression, it demonstrates superior reconstruction quality and computational efficiency on FFHQ, CelebA, and ImageNet relative to state-of-the-art baselines, with robust performance under varying noise levels and ablations. The approach also shows transferability of diffusion priors in out-of-distribution settings, highlighting practical impact for real-world 1-bit quantized inverse problems.

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.

Figures (11)

• Figure 1: Qualitative results of 1-bit CS on FFHQ images. We compare Diff-OneBit with QCS-SGM, SIM-DMIS and DiffPIR. Input images have an addtive Gaussian noise of $\sigma=0.5$.
• Figure 2: Qualitative results of 1-bit CS on CelebA images. We compare Diff-OneBit with SIM-DMIS. Input images have an additive Gaussian noise of $\sigma=0.5$ and $\sigma=1.5$.
• Figure 3: An illustration of the Diff-OneBit sampling step. At each reverse diffusion time $t$, we start with a noisy sample $\mathbf{\tilde{x}}_t$. First, the diffusion model acts as a denoiser to predict a preliminary clean image $\mathbf{\tilde{z}}_t$ (the prior update). This estimate is then corrected to a guided version $\hat{\mathbf{x}}_{0|t}$ by solving a data-consistency sub-problem using our differentiable surrogate likelihood. Finally, this guided estimate is used to compute the next state $\mathbf{\tilde{x}}_{t-1}$, advancing one step in the guided reverse diffusion.
• Figure 4: Qualitative results of 1-bit CS on FFHQ images. We compare Diff-OneBit under varying Gaussian noise levels in 1-bit CS.
• Figure 5: Qualitative results of logistic regression on FFHQ images. We compare Diff-OneBit under varying Gaussian noise levels in logistic regression.