Linear Inverse Problems

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9 papers1 paper in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Dual Flow: Joint Image-Measurement Flow for Inverse Problems
Nov 4, 2026Sevket Ege Yesilyurt, Figen S. OktemLinear Inverse Problems Inverse Problems
The Prior-Force Family of Implicit Denoiser Priors and Its Decisions in Linear Inverse Problems
Oct 30, 2026Weijie Liang, Chuling Wen, Jian LuLinear Inverse Problems Implicit Regularization
Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, 518060, China · National Center for Applied Mathematics Shenzhen (NCAMS), Shenzhen, 518055, China
SNaP: One-Step Posterior Sampling for Noisy Inverse Problems
Sep 28, 2026Shirin Shoushtari, Edward P. Chandler, Xiao Shi +1Flow Matching MeanFlow
WashU · UW-Madison
FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference
Sep 24, 2026Gatien Séguy, Thomas RodetDiffusion Model Guidance Bayesian Inverse Problems
SATIE
Posterior Information Dynamics of Diffusion Models for Linear Inverse Problems
Aug 22, 2026Xiangming MengLinear Inverse Problems Diffusion Models
ZJU-UIUC Institute, Zhejiang University Haining, Zhejiang 314400, China
Provable diffusion-based posterior sampling for linear inverse problems via DDIM
Jul 21, 2026Yuchen Jiao, Na Li, Changxiao Cai +2Diffusion Models for Image Restoration Bayesian Inverse Problems
Department of Statistics and Data Science, Chinese University of Hong Kong, Hong Kong · Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA · Department of Statistics and Data Science, the Wharton School, University of Pennsylvania, PA, USA
Exact Posterior Score Estimation for Solving Linear Inverse Problems
Jun 15, 2026Abbas Mammadov, Ozgur Kara, Kaan Oktay +5Diffusion Models for Image Restoration Diffusion-Based Inverse Problems
University of Oxford · UIUC · fal +1
Learning Normalized Energy Models for Linear Inverse Problems
May 15, 2026Nicolas Zilberstein, Santiago Segarra, Eero Simoncelli +1Bayesian Inverse Problems Energy-Based Models
Rice University, Houston, TX, USA · Flatiron Institute, New York, NY, USA · New York University, New York, NY, USA
P-Flow: Proxy-gradient Flows for Linear Inverse Problems
May 8, 2026Zehua Jiang, Fenghao Zhu, Xinquan Wang +2Flow Matching Inverse Problems
University of Notre Dame Indiana, USA

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Dual Flow: Joint Image-Measurement Flow for Inverse Problems

Sevket Ege Yesilyurt, Figen S. Oktem

Linear Inverse Problems Inverse Problems Image Inverse Problems Flow-Based Generative Modeling

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Existing generative model-based approaches to linear inverse problems typically use the acquired noisy measurement to condition or guide sampling in the image domain. In this work, we introduce Dual Flow, a novel joint flow model for solving linear inverse problems by jointly estimating the clean image and its corresponding noise-free measurement from the observation. Specifically, Dual Flow formulates image reconstruction and measurement denoising as a coupled estimation problem, using coupled flows in the image and measurement domains. The acquired noisy measurement

\mathbf{y}_0

is used only to initialize the measurement state; thereafter, the image and measurement states are jointly updated based on their current values. By construction, the final image and measurement estimates are guaranteed to satisfy the underlying forward model. We derive the sampling updates for the joint flow and show that they are governed by the conditional mean of the clean image given the current joint state. We further derive a closed-form expression for a sufficient statistic of the joint state and show that the required conditional mean can be obtained by solving an image-domain Gaussian denoising problem involving operator-dependent, correlated noise. We train a velocity-prediction network using this formulation to estimate the conditional mean from the derived sufficient statistic. Dual Flow requires no hyperparameter tuning beyond selecting the number of inference steps and achieves substantially shorter reconstruction times than competing methods. Extensive experiments across various linear inverse problems and image datasets demonstrate state-of-the-art performance in both distortion metrics and perceptual quality. Additional analyses assess robustness to model mismatch, as well as the ability to generate diverse plausible reconstructions and characterize reconstruction uncertainty.