Related papers: Learning Normalized Energy Models for Linear Inverse Problems

Learning Normalized Energy Models for Linear Inverse Problems

URL: http://arxiv.org/abs/2605.15487v1
Date: Fri, 15 May 2026 00:05:15 GMT
Title: Learning Normalized Energy Models for Linear Inverse Problems
Abstract summary: Generative diffusion models can provide powerful prior probability models for inverse problems in imaging.<n>Existing implementations suffer from two key limitations.<n>We introduce a new energy-based model trained for denoising with a covariance-based regularization term.
Score: 39.643595056992034
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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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