新能量模型让图像逆问题能精准推断,无需重训练。
Learning Normalized Energy Models for Linear Inverse Problems

- 用协方差正则化训练去噪能量模型,保持多测量条件一致
- 可直接计算归一化后验,支持多种图像修复任务
- 实现自适应采样、无偏修正和退化核盲估计
生成式扩散模型在成像逆问题中可提供强大先验,但现有方法存在两个关键局限:(i) 先验密度隐式表示,(ii) 依赖似然近似引入采样偏差。本文提出一种新型基于能量的模型,通过协方差正则化项训练去噪过程,确保不同观测条件下的结果一致性。该模型可直接计算多样化线性逆问题的归一化后验分布,无需额外微调或再训练。除保留扩散模型采样能力外,还首次实现能量引导的自适应采样(动态调整调度)、无偏马尔可夫链蒙特卡洛校正步骤,以及通过贝叶斯规则盲估计退化算子。在ImageNet、CelebA、AFHQ等多个数据集上,针对修补、去模糊等任务验证,性能优于或媲美现有基线。
原文摘要 · Abstract (English)
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.
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