Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study

2026-06-16 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

This paper presents the Langevin-within-Split Gibbs Sampler (LwSGS) as a unified and efficient alternative to the unadjusted Langevin algorithm (ULA) for Bayesian inverse problems, specifically image restoration. LwSGS leverages an asymptotically exact data augmentation (AXDA) to separate data-fitting and regularization terms, enabling efficient sampling from posterior distributions defined by explicit or computable score function-based priors. The framework accommodates diverse data-driven priors, including Regularization-by-Denoising (RED), Score-based Generative Models (SGM), Normalizing Flows (NF), and Convex-Ridge Regularizers (CRR). Experimental evaluations on image inpainting and single image super-resolution tasks, using FFHQ and ImageNet datasets, demonstrate LwSGS's consistently superior performance in reconstruction quality (PSNR, SSIM, LPIPS) and computational efficiency compared to ULA-based schemes. The method's practicability is further illustrated by restoring real-world geological images, highlighting its ability to enhance visual quality from suboptimal acquisitions.

Key takeaway

For Machine Learning Engineers developing Bayesian image restoration solutions, you should consider implementing the Langevin-within-Split Gibbs Sampler (LwSGS) framework. This method consistently outperforms ULA-based approaches in image quality and computational speed for tasks like inpainting and super-resolution. Its ability to integrate various score function-based priors and quantify uncertainty offers a robust, flexible alternative for high-dimensional inverse problems, especially with real-world, suboptimal data.

Key insights

LwSGS unifies diverse data-driven priors for Bayesian inverse problems by leveraging their score functions for efficient posterior sampling.

Principles

• Score functions unify diverse data-driven priors.
• AXDA improves MCMC mixing and scalability.
• LwSGS decouples likelihood and prior sampling.

Method

LwSGS uses asymptotically exact data augmentation to split posterior sampling into two conditional distributions, one of which is sampled via Langevin Monte Carlo using the prior score function.

In practice

• Apply LwSGS for image inpainting and super-resolution.
• Restore geological images from out-of-focus acquisitions.
• Quantify uncertainty with pixel-wise standard deviations.

Topics

• Bayesian Inverse Problems
• Langevin-within-SGS
• Score Function Priors
• Image Restoration
• Markov Chain Monte Carlo
• Data Augmentation
• Uncertainty Quantification

Code references

• cszn/DPIR
• FabianAltekrueger/patchNR
• yuanzhi-zhu/DiffPIR
• axgoujon/convex_ridge_regularizers

Best for: Computer Vision Engineer, AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.