# ANaLOG: Anisotropic Native-Latent Operator Guidance for Solving Inverse Problems

arXiv: https://arxiv.org/abs/2609.31933 · HTML: https://mlsanity.com/paper/2609.31933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 22 of its 36 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Improving the Diffusability of Autoencoders](https://mlsanity.com/paper/2502.14831/) (2025)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Estimating High Order Gradients of the Data Distribution by Denoising](https://mlsanity.com/paper/2111.04726/) (2021)
- [Readout Guidance: Learning Control from Diffusion Features](https://mlsanity.com/paper/2312.02150/) (2023)
- [Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance](https://mlsanity.com/paper/2402.02149/) (2024)
- [SILO: Solving Inverse Problems with Latent Operators](https://mlsanity.com/paper/2501.11746/) (2025)
- [Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costs](https://mlsanity.com/paper/2410.11149/) (2024)
- [Frequency-Guided Posterior Sampling for Diffusion-Based Image Restoration](https://mlsanity.com/paper/2411.15295/) (2024)

## Abstract (arXiv)

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.