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{this https URL}{ALPS}.
Abstract (translated)
解决成像中的逆问题需要支持高效推理、不确定性量化和原理性概率推理的模型。基于能量的模型（EBM）由于其可解释的能量景观和组合结构，非常适合这一任务，但历史上一直面临计算成本高和训练不稳定的缺点。为克服EBM的历史不足，我们引入了一种快速蒸馏策略，将预先训练好的扩散模型的优势转移到多尺度EBM中。这些经过蒸馏的EBM能够高效采样，并保持基于势能框架固有的可解释性和组合性。 利用EBM的组合特性，我们提出了一种用于最大后验概率（MAP）、最小均方误差（MMSE）和逆问题不确定性估计的退火Langevin后验抽样（ALPS）算法。与扩散模型使用的复杂潜在变量指导策略不同，我们在静态且可组合的良好定义后验分布上进行退火处理。 在图像修复和MRI重建实验中显示，我们的方法在精度和效率方面均可以匹敌或超越基于扩散的基线方法，并同时支持MAP恢复。总的来说，我们提出的框架为成像中的逆问题提供了一种可扩展且原理性的解决方案，在科学和临床环境中具有实际应用潜力。 ALPS代码可在GitHub仓库\href{this https URL}{ALPS}中获取。
URL
https://arxiv.org/abs/2601.02594
