Diffusion Model Based Signal Recovery Under 1-Bit Quantization
This work addresses a specific problem in signal processing and machine learning for tasks like image reconstruction under -bit quantization, offering an incremental improvement by adapting existing diffusion models to handle non-differentiable link functions.
The paper tackles the challenge of applying diffusion models to signal recovery under 1-bit quantization, such as in compressed sensing and logistic regression, by introducing Diff-OneBit, which uses a differentiable surrogate likelihood to enable gradient-based iterations and integrates with any pretrained diffusion model as a denoiser, resulting in high-fidelity reconstructed images that outperform state-of-the-art methods in quality and efficiency on datasets like FFHQ, CelebA, and ImageNet.
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.