# SILO: Solving Inverse Problems with Latent Operators

arXiv: https://arxiv.org/abs/2501.11746 · HTML: https://mlsanity.com/paper/2501.11746/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 37 of its 59 references that are in the map.
- First posted on arXiv 20 Jan 2025.

## Placed in

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

## Builds on (most cited first, 30 of 37)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [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)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)

## Built on by (most cited first, 19 of 19)

- [Compressed Image Generation with Denoising Diffusion Codebook Models](https://mlsanity.com/paper/2502.01189/) (2025)
- [Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation](https://mlsanity.com/paper/2504.18720/) (2025)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Turbo-DDCM: Fast and Flexible Zero-Shot Diffusion-Based Image Compression](https://mlsanity.com/paper/2511.06424/) (2025)
- [Inverse Problem Sampling in Latent Space Using Sequential Monte Carlo](https://mlsanity.com/paper/2502.05908/) (2025)
- [InverseCrafter: Efficient Video ReCapture as a Latent Domain Inverse Problem](https://mlsanity.com/paper/2512.05672/) (2025)
- [Consistency Regularised Gradient Flows for Inverse Problems](https://mlsanity.com/paper/2605.07907/) (2026)
- [Image Restoration via Diffusion Models with Dynamic Resolution](https://mlsanity.com/paper/2605.14267/) (2026)
- [Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers](https://mlsanity.com/paper/2601.04791/) (2026)
- [SP3: Spherical Priors for Plug-and-Play Restoration](https://mlsanity.com/paper/2606.16396/) (2026)
- [LatentINDIGO: An INN-Guided Latent Diffusion Algorithm for Image Restoration](https://mlsanity.com/paper/2505.12935/) (2025)
- [MACS: Measurement-Aware Consistency Sampling for Inverse Problems](https://mlsanity.com/paper/2510.02208/) (2025)
- [Align & Invert: Solving Inverse Problems with Diffusion and Flow-based Models via Representation Alignment](https://mlsanity.com/paper/2511.16870/) (2025)
- [Posterior Continuation with Noise-Conditioned Frequency Exposure for Diffusion Inverse Problems](https://mlsanity.com/paper/2602.00176/) (2026)
- [Accelerating Video Inverse Problem Solvers with Autoregressive Diffusion Models](https://mlsanity.com/paper/2605.20624/) (2026)
- [Music Restoration via Latent Operator Optimization and Diffusion Model Priors](https://mlsanity.com/paper/2608.01972/) (2026)
- [ANaLOG: Anisotropic Native-Latent Operator Guidance for Solving Inverse Problems](https://mlsanity.com/paper/2609.31933/) (2026)
- [LoCoVSR: Local Context Diffusion Posterior Sampling for Video Super-Resolution](https://mlsanity.com/paper/2609.32742/) (2026)
- [BAM! Bayesian Anything Model: a foundation model for generative computational imaging](https://mlsanity.com/paper/2609.39660/) (2026)

## Abstract (arXiv)

Consistent improvement of image priors over the years has led to the development of better inverse problem solvers. Diffusion models are the newcomers to this arena, posing the strongest known prior to date. Recently, such models operating in a latent space have become increasingly predominant due to their efficiency. In recent works, these models have been applied to solve inverse problems. Working in the latent space typically requires multiple applications of an Autoencoder during the restoration process, which leads to both computational and restoration quality challenges. In this work, we propose a new approach for handling inverse problems with latent diffusion models, where a learned degradation function operates within the latent space, emulating a known image space degradation. Usage of the learned operator reduces the dependency on the Autoencoder to only the initial and final steps of the restoration process, facilitating faster sampling and superior restoration quality. We demonstrate the effectiveness of our method on a variety of image restoration tasks and datasets, achieving significant improvements over prior art.