Image Inverse Problems

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10 papers in the last four weeks, up 150% on the four weeks before. 0.1% of all new papers.

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Latest papers 85

May 12, 2026cs.CV

Principled Design of Diffusion-based Optimizers for Inverse Problems

Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused across tasks without retraining, inference-time hyperparameters such as the noise schedule and posterior sampling weights typically require ad-hoc adjustment for each problem setup. We propose principled reparameterizations that induce invariances, allowing the same hyperparameters to be reused across multiple problems without re-tuning. In addition, building on the RED-diff framework, which reformulates posterior sampling as an optimization problem, we further develop the OptDiff pipeline. OptDiff provides a simplified tuning framework that facilitates the integration of convex optimization tools to accelerate inference. Experiments on image reconstruction, deblurring, and super-resolution show substantial speedups and improved image quality.

Julio Oscanoa, Irmak Sivgin, Cagan Alkan +4

Department of Bioengineering · Deparment of Electrical Engineering · Department of Radiology, Stanford University, USA.

Inference-Time Optimization Diffusion-Based Inverse Problems Diffusion Posterior Sampling Diffusion Model Inference Acceleration Inverse Problems Image Inverse Problems

May 11, 2026eess.IV

A Stability Benchmark of Generative Regularizers for Inverse Problems

Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect settings. Typical definitions of stability encompass the notion of ''convergent regularization'', robustness to out-of-distribution data, and to inaccuracies in the forward operator or noise model. We evaluate these properties numerically. Furthermore, we benchmark generative approaches against modern optimization-based methods inspired by the widely used variational techniques. Our results give insights for which settings and applications generative priors can deliver state-of-the-art reconstructions, and on those in which they fall short or may even be problematic.

Alexander Denker, Johannes Hertrich, Sebastian Neumayer

Helmholtz Imaging, Deutsches Elektronen-Synchrotron DESY, Germany · ENS Paris & Inria, France · Chemnitz University of Technology, Germany

Generative Modeling Diffusion-Based Inverse Problems Inverse Problems Diffusion Models Image Inverse Problems

May 10, 2026cs.CV

Dual-Path Hyperprior Informed Deep Unfolding Network for Image Compressive Sensing

Recent Deep Unfolding Networks (DUNs) have significantly advanced Compressive Sensing (CS) by integrating iterative optimization with deep networks. However, existing DUNs still suffer from two challenges: 1) Reliance on a single measurement stream, which limits effective information interaction across distinct measurement subsets. 2) Uniform processing of all image regions, which overlooks varying reconstruction difficulties induced by diverse textures. To address these limitations, a novel Dual-Path Hyperprior Informed Deep Unfolding Network (DPH-DUN) is proposed, which partitions measurements into double subsets to enable hyperprior-guided reconstruction via a dual-path architecture. In the Deep Hyperprior Learning branch, a series of lightweight neural modules are designed to efficiently generate hyperprior knowledge of different domains, enabling collaborative guidance for the CS reconstruction. In the Hyperprior Informed Reconstruction branch, a deep unfolding framework with hyperprior guidance is constructed to iteratively refine reconstruction. Specifically, i) in the gradient descent step, a Hyperprior Informed Step Size Generation network is designed to dynamically generate spatially varying step maps, enabling adaptive fine-grained gradient updates. ii) In the proximal mapping step, two well-designed hyperprior informed attention mechanisms are introduced to dynamically focus on challenging regions via gradient-based hard and soft attentions, facilitating CS reconstruction accuracy. Extensive experiments demonstrate that the proposed DPH-DUN outperforms existing CS methods.

Tianyi Lu, Wenxue Cui, Shaohui Liu

Harbin Institute of Technology

Image Reconstruction Image Inverse Problems

May 10, 2026cs.CV

Outlier-Robust Diffusion Solvers for Inverse Problems

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases.

Yang Zheng, Jiahua Liu, Tongyao Pang +2

School of Computer Science and Engineering, University of Electronic Science and Technology of China · Yau Mathematical Sciences Center, Tsinghua University

Diffusion Models for Image Restoration Robust Optimization Diffusion-Based Inverse Problems Inverse Problems Image Inverse Problems

May 8, 2026cs.LG

P-Flow: Proxy-gradient Flows for Linear Inverse Problems

Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate differentiating through unrolled paths, leading to numerical instability and prohibitive computational overhead. To address this, we propose P-Flow, a framework that stabilizes the reconstruction process by leveraging a proxy gradient to update the source point. This approach effectively circumvents the numerical instability and memory overhead of long-chain differentiation. To ensure consistency with the prior distribution, we employ a Gaussian spherical projection motivated by the concentration of measure phenomenon in high-dimensional spaces. We further provide a theoretical analysis for P-Flow based on Bayesian theory and Lipschitz continuity. Experiments across diverse restoration tasks demonstrate that P-Flow delivers competitive performance, especially under extreme degradations such as severely ill-posed conditions and high measurement noise.

Zehua Jiang, Fenghao Zhu, Xinquan Wang +2

University of Notre Dame Indiana, USA

Flow Matching Inverse Problems Image Inverse Problems

May 8, 2026stat.ML

Consistency Regularised Gradient Flows for Inverse Problems

Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations (NFEs) and backpropagation through large pretrained components, leading to substantial computational costs and, in some cases, degraded reconstruction quality. We propose a unified Euclidean-Wasserstein-2 gradient-flow framework that jointly performs posterior sampling and prompt optimization in the latent space through a single flow that aligns the prior and posterior with the observed data. Combined with few-step latent text-to-image models, this formulation enables low-NFE inference without backpropagation through autoencoders. Experiments across several canonical imaging inverse problems show that our method achieves state-of-the-art performance with significantly reduced computational cost.

Alessio Spagnoletti, Tim Y. J. Wang, Marcelo Pereyra +1

Laboratoire MAP5, UMR 8145, Université Paris Cité, CNRS · Department of Mathematics, Imperial College London · Heriot-Watt University, MACS & Maxwell Institute

Latent Diffusion Models Wasserstein Gradient Flows Diffusion-Based Inverse Problems Flow-Based Generative Modeling Diffusion Posterior Sampling Image Inverse Problems

May 5, 2026cs.CV

Conditions for well-posed color recovery in scattering media

Recovering scene color from images captured in scattering media is a fundamental inverse problem in optical imaging. Yet the problem is intrinsically ill-posed as multiple solutions can explain the same observation, and prediction error cannot be controlled without understanding the space of candidate solutions. Here, we present sufficient conditions under which color recovery in a scattering medium becomes well-posed. Observing that ill-posedness stems from (i) projection of spectral signals onto pixel intensities, and (ii) unknown medium parameters, we demonstrate that sensor improvements alone cannot resolve medium-induced distortions without additional constraints. We identify recovery patterns, cross-pixel relationships that naturally occur in images, and prove, for an ideal hyperspectral camera, that they restrict the solution to a unique candidate. This opens the door to a new class of vision algorithms grounded in first principles, enabling quantitative analysis of images in scattering environments.

Grigory Solomatov, Derya Akkaynak

Hatter Department of Marine Technologies, University of Haifa, Haifa, Israel · Interuniversity Institute for Marine Sciences, Eilat, Israel

Image Restoration Inverse Problems Image Inverse Problems

Apr 29, 2026eess.IV

Circular Phase Representation and Geometry-Aware Optimization for Ptychographic Image Reconstruction

Traditional iterative reconstruction methods are accurate but computationally expensive, limiting their use in high-throughput and real-time ptychography. Recent deep learning approaches improve speed, but often predict phase as a Euclidean scalar despite its

2π

periodicity, which can introduce wrapping artifacts, discontinuities at

\pmπ

, and a mismatch between the loss and the underlying signal geometry. We present a deep learning framework for ptychographic reconstruction that models phase on the unit circle using cosine and sine components. Phase error is optimized with a differentiable geodesic loss, which avoids branch-cut discontinuities and provides bounded gradients. The network further incorporates saturation-aware dual-gain input scaling, parallel encoder branches, and three decoders for amplitude, cosine, and sine prediction, together with a composite loss that promotes circular consistency and structural fidelity. Experiments on synthetic and experimental datasets show consistent improvements in both amplitude and phase reconstruction over existing deep learning methods. Frequency-domain analysis further shows better preservation of mid- and high-frequency phase content. The proposed method also provides substantial speedup over iterative solvers while maintaining physically consistent reconstructions.

Carson Yu Liu, Jun Cheng, Chien-Chun Chen +1

School of Electrical and Computer Engineering, University of Sydney, Camperdown, NSW 2006, Australia · Institute for Infocomm Research, Agency for Science, Technology and Research (A*STAR), Singapore 138632 · Department of Engineering and System Science, National Tsing Hua University, Hsinchu 300044, Taiwan

Image Reconstruction Image Inverse Problems

Apr 26, 2026eess.IV

GS-DOT: Gaussian splatting-based image reconstruction for diffuse optical tomography

This work presents GS-DOT, a novel image reconstruction framework based on Gaussian Splatting (GS) for diffuse optical tomography (DOT). Inspired by GS for rendering applications, absorption coefficients are represented as a sparse sum of anisotropic Gaussian primitives optimized to fit measured time-resolved point-spread functions through analytic gradients and Adam optimization. This is the first adaptation of GS algorithms in the photon diffusion regime, where the ray transport function is replaced by the diffusion functions to enable accurate modeling of light transport in highly scattering media. Validation on synthetic tissue models demonstrate high accuracy in localization and quantification of reconstructed absorption maps for both clean and noisy signals. GS-DOT has demonstrated high robustness to noise and showed a huge reduction in memory demand.

Jingjing Jiang

Computational Optical Imaging Group, Biomedical Optics Research Laboratory, Dept. of Neonatology, University Hospital Zurich and University of Zurich, Switzerland

Medical Imaging Image Reconstruction Gaussian Splatting Image Inverse Problems

Apr 23, 2026cs.CV

Multiscale Super Resolution without Image Priors

We address the ambiguities in the super-resolution problem under translation. We demonstrate that combinations of low-resolution images at different scales can be used to make the super-resolution problem well posed. Such differences in scale can be achieved using sensors with different pixel sizes (as demonstrated here) or by varying the effective pixel size through changes in optical magnification (e.g., using a zoom lens). We show that images acquired with pairwise coprime pixel sizes lead to a system with a stable inverse, and furthermore, that super-resolution images can be reconstructed efficiently using Fourier domain techniques or iterative least squares methods. Our mathematical analysis provides an expression for the expected error of the least squares reconstruction for large signals assuming i.i.d. noise that elucidates the noise-resolution tradeoff. These results are validated through both one- and two-dimensional experiments that leverage charge-coupled device (CCD) hardware binning to explore reconstructions over a large range of effective pixel sizes. Finally, two-dimensional reconstructions for a series of targets are used to demonstrate the advantages of multiscale super-resolution, and implications of these results for common imaging systems are discussed.

Daniel Fu, Gabby Litterio, Pedro Felzenszwalb +1

Division of Applied Mathematics (Fu) and School of Engineering (Litterio, Felzenszwalb, Zia), Brown University, Providence, RI, 02906.

Image Super-Resolution Image Inverse Problems

Apr 21, 2026eess.IV

Deep Image Prior for photoacoustic tomography can mitigate limited-view artifacts

We study the deep image prior (DIP) framework applied to photoacoustic tomography (PAT) as an unsupervised reconstruction approach to mitigate limited-view artifacts and noise commonly encountered in experimental settings. Efficient implementation is achieved by employing recently published fast forward and adjoint algorithms for circular measurement geometries. Initialization via a fast inverse and total variation (TV) regularization are applied to further suppress noise and mitigate overfitting. For comparison, we compute a classical TV reconstruction. Our experiments comprise simulated PAT measurements under limited-view geometries and varying levels of added noise as well as experimental measurements together with using a digital twin for quality assessment. Our findings suggest that DIP framework provides an effective unsupervised strategy for robust PAT reconstruction even in the challenging case of a limited view geometry providing improvement in several quantitative measures over total variation reconstructions.

Hanna Pulkkinen, Jenni Poimala, Leonid Kunyansky +2

1Research Unit of Mathematical Sciences, University of Oulu, Finland · Department of Technical Physics, University of Eastern Finland, Finland · Department of Mathematics, University of Arizona, USA +2

Medical Imaging Image Reconstruction Computational Imaging Image Inverse Problems

Apr 18, 2026cs.LG

Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning

Diffusion models (DMs) have recently shown remarkable performance on inverse problems (IPs). Optimization-based methods can fast solve IPs using DMs as powerful regularizers, but they are susceptible to local minima and noise overfitting. Although DMs can provide strong priors for Bayesian approaches, enforcing measurement consistency during the denoising process leads to manifold infeasibility issues. We propose Noise-space Hamiltonian Monte Carlo (N-HMC), a posterior sampling method that treats reverse diffusion as a deterministic mapping from initial noise to clean images. N-HMC enables comprehensive exploration of the solution space, avoiding local optima. By moving inference entirely into the initial-noise space, N-HMC keeps proposals on the learned data manifold. We provide a comprehensive theoretical analysis of our approach and extend the framework to a noise-adaptive variant (NA-NHMC) that effectively handles IPs with unknown noise type and level. Extensive experiments across four linear and three nonlinear inverse problems demonstrate that NA-NHMC achieves superior reconstruction quality with robust performance across different hyperparameters and initializations, significantly outperforming recent state-of-the-art methods. The code is available at https://github.com/NA-HMC/NA-HMC.

Yingzhi Xia, Setthakorn Tanomkiattikun, Liangli Zhen +1

Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore · Agency for Science, Technology and Research, Singapore · Johns Hopkins University +1

Markov Chain Monte Carlo Bayesian Inverse Problems Diffusion Sampling Diffusion-Based Inverse Problems Diffusion Posterior Sampling Image Inverse Problems

Apr 17, 2026cs.CV

SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

Markus Haltmeier, Lukas Neumann, Nadja Gruber +1

Self-Supervised Learning Sparse-View CT Reconstruction Computed Tomography Inverse Problems Image Inverse Problems

Mar 2, 2026cs.CV

3D Field of Junctions: A Noise-Robust, Training-Free Structural Prior for Volumetric Inverse Problems

Volume denoising is a foundational problem in computational imaging, as many 3D imaging inverse problems face high levels of measurement noise. Inspired by the strong 2D image denoising properties of Field of Junctions (ICCV 2021), we propose a novel, fully volumetric 3D Field of Junctions (3D FoJ) representation that optimizes a junction of 3D wedges that best explain each 3D patch of a full volume, while encouraging consistency between overlapping patches. In addition to direct volume denoising, we leverage our 3D FoJ representation as a structural prior that: (i) requires no training data, and thus precludes the risk of hallucination, (ii) preserves and enhances sharp edge and corner structures in 3D, even under low signal to noise ratio (SNR), and (iii) can be used as a drop-in denoising representation via projected or proximal gradient descent for any volumetric inverse problem with low SNR. We demonstrate successful volume reconstruction and denoising with 3D FoJ across three diverse 3D imaging tasks with low-SNR measurements: low-dose X-ray computed tomography (CT), cryogenic electron tomography (cryo-ET), and denoising point clouds such as those from lidar in adverse weather. Across these challenging low-SNR volumetric imaging problems, 3D FoJ outperforms the evaluated classical denoisers, untrained neural denoisers, and denoisers trained only on noisy examples. Code is available at https://github.com/voilalab/3D-Field-of-Junctions.

Narges Moeini, Namhoon Kim, Justin Romberg +1

Georgia Institute of Technology

Image Inverse Problems Image Denoising

Feb 10, 2026cs.CV

Allure of Craquelure: A Variational-Generative Approach to Crack Detection in Paintings

Recent advances in imaging technologies, deep learning and numerical performance have enabled non-invasive detailed analysis of artworks, supporting their documentation and conservation. In particular, automated detection of craquelure in digitized paintings is crucial for assessing degradation and guiding restoration, yet remains challenging due to the possibly complex scenery and the visual similarity between cracks and crack-like artistic features such as brush strokes or hair. We propose a hybrid approach that models crack detection as an inverse problem, decomposing an observed image into a crack-free painting and a crack component. A deep generative model is employed as powerful prior for the underlying artwork, while crack structures are captured using a Mumford--Shah-type variational functional together with a crack prior. Joint optimization yields a pixel-level map of crack localizations in the painting.

Laura Paul, Holger Rauhut, Martin Burger +2

Dept. of Mathematics, LMU Munich, Germany · Munich Center for Machine Learning, Germany · Helmholtz Imaging, Deutsches Elektronen-Synchrotron DESY, Germany +2

Crack Segmentation Image Inverse Problems Anomaly Detection

Feb 9, 2026eess.IV

Trajectory Stitching for Solving Inverse Problems with Flow-Based Models

Flow-based generative models have emerged as powerful priors for solving inverse problems. One option is to directly optimize the initial latent code (noise), such that the flow output solves the inverse problem. However, this requires backpropagating through the entire generative trajectory, incurring high memory costs and numerical instability. We propose MS-Flow, which represents the trajectory as a sequence of intermediate latent states rather than a single initial code. By enforcing the flow dynamics locally and coupling segments through trajectory-matching penalties, MS-Flow alternates between updating intermediate latent states and enforcing consistency with observed data. This reduces memory consumption while improving reconstruction quality. We demonstrate the effectiveness of MS-Flow over existing methods on image recovery and inverse problems, including inpainting, super-resolution, and computed tomography.

Alexander Denker, Zeljko Kereta, Carola-Bibiane Schönlieb +1

Department of Computer Science, University College London · Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

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

Jan 29, 2026cs.LG

Inverse Problems Conditioned on Observation Ensembles: Applications and Methods

We introduce a new multivariate statistical problem that we refer to as the Ensemble-conditioned Inverse Problem (EIP). The aim of EIP is to invert for an ensemble that is distributed according to the pushforward of a prior under a forward process. In high energy physics (HEP), this is related to a widely known problem called unfolding, which aims to reconstruct the true physics distribution from observations that are distorted by detector effects. The EIP also arises in full waveform inversion (FWI) and inverse imaging with unknown priors. We propose non-iterative inference-time methods that construct posterior samplers based on a new class of conditional generative models, which we call ensemble inverse generative models. For the posterior modeling, these models additionally use the ensemble information contained in the observation set on top of single observations. Unlike existing methods, our proposed methods avoid explicit and iterative use of the forward model at inference time via training across several sets of truth-observation pairs that are consistent with the same forward model, but originate from a wide range of priors. We empirically demonstrate that this training procedure can implicitly encode the likelihood model, enabling direct posterior inference for unseen priors to some degree. We benchmark the proposed method on several synthetic and real datasets in inverse imaging, HEP, and FWI. Our code is available at https://github.com/ZhengyanHuan/EIP.

Zhengyan Huan, Camila Pazos, Martin Klassen +3

Department of Electrical and Computer Engineering, Tufts University, Medford, Massachusetts · The NSF AI Institute for Artificial Intelligence and Fundamental Interactions · Department of Physics and Astronomy, Tufts University, Medford, Massachusetts +1

Posterior Sampling Inverse Problems Image Inverse Problems

Dec 9, 2025eess.IV

Learned iterative networks: An operator learning perspective

Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation algorithms for solving variational problems. While the underlying algorithm is usually formulated in the functional analytic setting, learned approaches are often viewed as purely discrete. In this survey we present a unified operator view for learned iterative networks. Specifically, we formulate a learned reconstruction operator, defining how to compute, and separately the learning problem, which defines what to compute. In this setting we present common approaches and show that many approaches are closely related in their core. We review linear as well as non-linear inverse problems in this framework and present a short numerical study to conclude.

Andreas Hauptmann, Ozan Öktem

Research Unit of Mathematical Sciences, University of Oulu, Finland · Department of Computer Science, University College London, United Kingdom · Department of Mathematics, KTH - Royal Institute of Technology, Sweden

Image Reconstruction Computational Imaging Algorithm Unrolling Operator Learning Image Inverse Problems

Nov 23, 2025cs.CV

Jacobian-Aware Posterior Sampling for Inverse Problems

Diffusion models provide powerful generative priors for solving inverse problems by sampling from a posterior distribution conditioned on corrupted measurements. Existing methods primarily follow two paradigms: direct methods, which approximate the likelihood term, and proximal methods, which incorporate intermediate solutions satisfying measurement constraints into the sampling process. Under standard Gaussian approximations and locally-linear measurements, we demonstrate that these approaches differ fundamentally in their treatment of the diffusion denoiser's Jacobian within the likelihood term. While this Jacobian encodes critical prior knowledge of the data distribution, training-induced non-idealities can degrade performance in zero-shot settings. In this work, we bridge direct and proximal approaches by proposing a principled Jacobian-Aware Posterior Sampler (JAPS). JAPS leverages the Jacobian's prior knowledge while mitigating its detrimental effects through a corresponding proximal solution, requiring no additional computational cost. Additionally, we integrate our guidance into DDIM sampling, with a corrected conditional factor that has been missing in previous works. Our method enhances reconstruction quality across diverse linear and nonlinear noisy imaging tasks, outperforming existing diffusion-based baselines in perceptual quality while maintaining or improving distortion metrics.

Liav Hen, Tom Tirer, Raja Giryes +1

Tel Aviv University, Israel · Bar-Ilan University, Israel · University of Cambridge, UK

Bayesian Inverse Problems Diffusion Guidance Diffusion-Based Inverse Problems Diffusion Posterior Sampling Image Inverse Problems

Nov 21, 2025cs.AI

DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing

From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior: the prior offers limited guidance, while reconstruction is largely driven by the measurement-consistency term, leading to an inference process that is effectively decoupled from the diffusion dynamics. We show that the diffusion prior in these solvers functions primarily as a warm initializer that places estimates near the data manifold, while reconstruction is driven almost entirely by measurement consistency. Based on this observation, we introduce \textbf{DAPS++}, which fully decouples diffusion-based initialization from likelihood-driven refinement, allowing the likelihood term to guide inference more directly while maintaining numerical stability and providing insight into why unified diffusion trajectories remain effective in practice. By requiring fewer function evaluations (NFEs) and measurement-optimization steps, \textbf{DAPS++} achieves high computational efficiency and robust reconstruction performance across diverse image restoration tasks.

Hao Chen, Renzheng Zhang, Scott S. Howard

University of Notre Dame, Notre Dame, IN 46556, USA

Diffusion Models for Image Restoration Bayesian Inverse Problems Diffusion-Based Inverse Problems Diffusion Posterior Sampling Diffusion Model Inference Acceleration Image Inverse Problems

Oct 2, 2025eess.IV

MACS: Measurement-Aware Consistency Sampling for Inverse Problems

Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency Models (CMs) address this limitation by enabling high-quality generation in only one or a few steps, their direct application to inverse problems has remained largely unexplored. This paper introduces a modified consistency sampling framework specifically designed for inverse problems. The proposed approach regulates the sampler's stochasticity through a measurement-consistency mechanism that leverages the degradation operator, thereby enforcing fidelity to the observed data while preserving the computational efficiency of consistency-based generation. Comprehensive experiments on the Fashion-MNIST and LSUN Bedroom datasets demonstrate consistent improvements across both perceptual and pixel-level metrics, including the Fréchet Inception Distance (FID), Kernel Inception Distance (KID), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM), compared with baseline consistency and diffusion-based sampling methods. The proposed method achieves competitive or superior reconstruction quality with only a small number of sampling steps.

Amirreza Tanevardi, Pooria Abbas Rad Moghadam, Seyed Mohammad Eshtehardian +2

Department of Electrical Engineering Sharif University of Technology Tehran, Iran · Electronics Research Institute Sharif University of Technology Tehran, Iran

Diffusion Model Sampling Inverse Problems Consistency Models Image Inverse Problems

Sep 18, 2025eess.IV

Breaking the Weak Recovery Limit in Random Phase Retrieval with Learned Regularizers

We seek to recover an unknown signal from nonlinear amplitude-only measurements, a challenging inverse problem. Strong theoretical guarantees have been established for idealized random measurements, defining the sampling ratio required for signal recovery. However, these results neglect signal priors, which can fundamentally shift these limits, potentially enabling reconstruction with far fewer measurements and simpler models. We evaluate a variety of image priors in the context of severe undersampling with physically-grounded random measurement models. Our results show that these priors enable accurate recovery well below the weak recovery limit, the theoretical threshold required for recovery better than a random guess.

Stanislas Ducotterd, Zhiyuan Hu, Michael Unser +1

Biomedical Imaging Group, ´Ecole Polytechnique F´ed´erale de Lausanne

Image Inverse Problems

Aug 4, 2025cs.CV

A Morse-Bott Framework for Blind Inverse Problems: Local Recovery Guarantees and the Failure of the MAP

Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a posterior distribution. In applications such as blind deblurring, this principle is used to recover sharp images from degraded observations. In this paper, we analyze the recovery guarantees of MAP-based methods by adopting a \emph{Morse--Bott framework}. We model the image potential as a Morse--Bott function, where natural images are modeled as residing locally on a critical submanifold. This means that while the potential is locally flat along the

natural'' directions of the image manifold, it is strictly convex in the directions normal to it. We demonstrate that this Morse--Bott hypothesis aligns with the structural properties of state-of-the-art learned priors, a finding we validate through an experimental analysis of the potential landscape and its Hessian spectrum. Our theoretical results show that, in a neighborhood of the ground-truth image and operator, the posterior admits local minimizers that are stable both with respect to initialization (gradient descents converge to the same minimizer) and to small perturbations of the data (solutions vary smoothly with the observations). This local stability potentially provides a theoretical justification for the empirical success of well designed gradient-based optimization in these settings. However, we also demonstrate that this local stability is a \textbf{local} property: the

blurry trap'', well-known for sparse priors in blind deconvolution, persists even with state-of-the-art learned priors. Our findings demonstrate that the failure of MAP in blind deconvolution is not a limitation of prior quality, but an intrinsic characteristic of the landscape. We conclude that successful recovery depends on strategic initialization around favorable local minima.

Minh-Hai Nguyen, Edouard Pauwels, Pierre Weiss

IRIT, Toulouse University, Toulouse, France · Toulouse School of Economics, Universit´e Toulouse Capitole et IUF, Toulouse, France

Image Deblurring Bayesian Inference Image Inverse Problems

May 29, 2025cs.LG

EquiReg: Equivariance Regularized Diffusion for Inverse Problems

Diffusion models represent the state-of-the-art for solving inverse problems such as image restoration tasks. Diffusion-based inverse solvers incorporate a likelihood term to guide prior sampling, generating data consistent with the posterior distribution. However, due to the intractability of the likelihood, most methods rely on isotropic Gaussian approximations, which can push estimates off the data manifold and produce inconsistent, poor reconstructions. We propose Equivariance Regularized (EquiReg) diffusion, a general plug-in framework that improves posterior sampling by penalizing trajectories that deviate from the data manifold. EquiReg formalizes manifold-preferential equivariant functions that exhibit low equivariance error for on-manifold samples and high error for off-manifold ones, thereby guiding sampling toward symmetry-preserving regions of the solution space. We highlight that such functions naturally emerge when training non-equivariant models with augmentation or on data with symmetries. EquiReg's largest gains are under reduced sampling and measurement consistency steps, where many methods suffer severe quality degradation. By regularizing trajectories toward the manifold, EquiReg implicitly accelerates convergence and enables high-quality reconstructions. EquiReg consistently improves performance in linear and nonlinear image restoration tasks and solving partial differential equations. Our code is available at https://github.com/Anima-Lab/EquiReg

Bahareh Tolooshams, Aditi Chandrashekar, Rayhan Zirvi +4

University of Alberta · Alberta Machine, Intelligence Institute (Amii) · Neuroscience and Mental Health Institute, University of Alberta +3

Diffusion Models for Image Restoration Diffusion-Based Inverse Problems Diffusion Posterior Sampling PDE Inverse Problems Image Inverse Problems

Dec 3, 2024cs.CV

Filterless Snapshot Hyperspectral Imaging using Guided Patch Diffusion

We consider the problem of reconstructing a HxWx31 hyperspectral image from a

H\times W

grayscale snapshot measurement that is captured using only a single diffractive lens and a filterless panchromatic photosensor. This problem is severely ill-posed, but we present a model that produces high-quality results in simulation and experiment. We make efficient use of limited training data by creating a conditional denoising diffusion model that operates on small patches in a shift-invariant manner. During inference, we synchronize per-patch hyperspectral predictions using guidance by physical consistency with the system's optical point spread function. Our experiments reveal that the patch size can be as small as the point spread function, with local optical cues being the main source of information about complete spectra. Also, by drawing multiple samples, our model provides per-pixel uncertainty estimates that strongly correlate with reconstruction error.

Dean Hazineh, Luca Sacchi, Davide Cassara +2

Harvard University

Diffusion Model Guidance Physics-Guided Image Restoration Hyperspectral Imaging Computational Imaging Diffusion-Based Inverse Problems Diffusion Models+1