Problem
Research questions and friction points this paper is trying to address.
inverse problems
latent diffusion models
native-latent guidance
anisotropic uncertainty
sampling errors
ANaLOG: Anisotropic Native-Latent Operator Guidance for Solving Inverse Problems
🤖 AI Summary
This study addresses the limitation of existing latent diffusion models in solving inverse problems, where isotropic guidance neglects directional discrepancies and variations in prediction reliability. This work proposes ANaLOG, a framework that models uncertainty by learning anisotropic, input- and time-dependent covariance matrices to enable efficient perceptual guidance. Furthermore, it provides the first theoretical proof establishing the necessity of anisotropic weighting for correct sampling, revealing the inherent sampling errors introduced by isotropic guidance. By integrating latent-space surrogate models with uncertainty quantification techniques, the proposed method significantly enhances perceptual reconstruction quality across five challenging classes of inverse problems while maintaining computational efficiency.
📝 Abstract
Native-latent guidance is a recent paradigm for solving inverse problems with latent diffusion models. It replaces repeated evaluations of the image-space forward model, each requiring a decoder pass, with efficient guidance computed using a learned latent-space surrogate. However, existing methods apply guidance uniformly across latent dimensions, ignoring that measurements are informative only along certain directions and that the reliability of model predictions varies across inputs and timesteps. We propose ANaLOG, a framework for efficient uncertainty-aware guidance with pretrained latent diffusion models. ANaLOG models uncertainty by learning an anisotropic, input- and time-dependent covariance that is integrated into the guidance mechanism to emphasize reliable directions and downweight uncertain ones. We theoretically analyze this framework in a linear model setting and prove that anisotropic, uncertainty-aware weighting is necessary for correct sampling, whereas isotropic guidance induces sampling errors. Experiments across five challenging inverse problems show that ANaLOG improves perceptual reconstruction quality over existing methods while preserving efficiency.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Anisotropic Guidance
Latent Diffusion Models
Inverse Problems
Uncertainty-aware
Native-latent Operator
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