Annealed Langevin Posterior Sampling (ALPS): A Rapid Algorithm for Image Restoration with Multiscale Energy Models

2026-01-05

AI Summary

This work addresses the challenges of high computational cost, training instability, inefficient inference, and difficulty in uncertainty quantification inherent in energy-based models for image inverse problems. The authors propose a multi-scale energy modeling approach based on fast distillation of diffusion models and introduce ALPS, a sampling strategy that combines annealed Langevin dynamics with a static posterior distribution. This method is the first to leverage diffusion distillation to construct efficient, composable multi-scale energy models capable of supporting both MAP and MMSE estimation as well as uncertainty quantification. Experiments on image inpainting and MRI reconstruction demonstrate that ALPS matches or exceeds diffusion model baselines in both accuracy and efficiency, offering a theoretically sound and practically effective solution.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Solving inverse problems in imaging requires models that support efficient inference, uncertainty quantification, and principled probabilistic reasoning. Energy-Based Models (EBMs), with their interpretable energy landscapes and compositional structure, are well-suited for this task but have historically suffered from high computational costs and training instability. To overcome the historical shortcomings of EBMs, we introduce a fast distillation strategy to transfer the strengths of pre-trained diffusion models into multi-scale EBMs. These distilled EBMs enable efficient sampling and preserve the interpretability and compositionality inherent to potential-based frameworks. Leveraging EBM compositionality, we propose Annealed Langevin Posterior Sampling (ALPS) algorithm for Maximum-A-Posteriori (MAP), Minimum Mean Square Error (MMSE), and uncertainty estimates for inverse problems in imaging. Unlike diffusion models that use complex guidance strategies for latent variables, we perform annealing on static posterior distributions that are well-defined and composable. Experiments on image inpainting and MRI reconstruction demonstrate that our method matches or surpasses diffusion-based baselines in both accuracy and efficiency, while also supporting MAP recovery. Overall, our framework offers a scalable and principled solution for inverse problems in imaging, with potential for practical deployment in scientific and clinical settings. ALPS code is available at the GitHub repository \href{https://github.com/JyoChand/ALPS}{ALPS}.

Problem

• inverse problems
• energy-based models
• image restoration
• computational efficiency
• uncertainty quantification

Innovation

• Energy-Based Models
• Posterior Sampling
• Annealed Langevin Dynamics
• Diffusion Distillation
• Inverse Problems