Diffusion-Based Inverse Problems

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15 papers in the last four weeks, up 400% on the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 89

Oct 7, 2026cs.LG

Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps

Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, non-differentiable forward models remain hard. We introduce diffusion waltz, an MCMC method using SDEdit-style noising-denoising as a proposal, corrected via Metropolis-Hastings for exact posterior sampling without prior evaluation. We further propose injecting observations into the proposal while preserving exactness, using a gradient-free ensemble Kalman update. On a non-differentiable Navier-Stokes initial condition recovery task, diffusion waltz outperforms existing baselines across different noise and nonlinearity regimes.

So Takao, Gregory David Bellchambers, Luke Ye +2

PhysicsX London, UK

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

Oct 7, 2026eess.AS

VM-ARRAYDPS: Virtual Microphone Augmented Diffusion Posterior Sampling for Unsupervised Blind Speech Separation

Blind Source Separation(BSS) is a fundamental problem in signal processing, aiming to separate multiple source signals from their mixtures without prior knowledge of the sources or the mixing process. Traditional approaches, such as Independent Vector Analysis (IVA) exploits statistical independence of sources. Recently, diffusion-based approaches have emerged as a promising alternative by leveraging powerful generative priors. Among them, ArrayDPS formulates BSS problem as a posterior sampling problem, and utilizes a pretrained speech diffusion model to guide the recovery of clean source signals. A key factor behind its separation capability is the multi-channel consistency (MC) objective, which enforces the estimated source signals to reconstruct the observed microphone mixtures through the estimated acoustic transfer functions. However, the number of microphones in the array is often limited, which constrains the performance of ArrayDPS. To address this issue, we propose VM-ArrayDPS, a novel method that augments the microphone array with virtual microphones with higher-SNR, these microphones can offer extra MC constraints to enhance the separation performance. Experimental results demonstrate that VM-ArrayDPS significantly outperforms ArrayDPS on both 2-speaker and 3-speaker datasets, showcasing the effectiveness of virtual microphone augmentation in improving BSS performance. We also did ablation studies to show the influence of the number of virtual microphones and weight of the MC objective brought by virtual microphones.

Jingqi Sun, Haozhan Tang, Shulin He +1

Department of Computer Science and Engineering Southern University of Science and Technology, Shenzhen, China

Speech Separation Diffusion-Based Inverse Problems Audio Diffusion Models

Oct 7, 2026cs.CV

PhyDiCT: Plug-and-Play CT Reconstruction from Sparse X-Rays via Differentiable Rendering and Strong Priors

Reconstructing 3D Computed Tomography (CT) images from a few X-ray projections is a highly ill-posed inverse problem due to the loss of volumetric information. We propose PhyDiCT, a training-free framework that integrates a differentiable Physics-based forward model, grounded in the Beer-Lambert law, with a text-conditioned Diffusion as a strong prior to reconstruct 3D lung CT images. We refer to our approach as training-free since the prior model is used without fine-tuning, and our goal is to steer the denoising procedure to generate samples consistent with X-ray observations. We guide the diffusion generation using Split Gibbs sampling to jointly optimize for projection fidelity (reward) and consistency with prior knowledge. Also, we introduce a test-time refinement step that enhances image realism and anatomical coherence. We extensively evaluate our method on publicly available 3D CT datasets using both perceptual and semantic metrics, demonstrating that it surpasses existing plug-and-play diffusion and fully trained reconstruction approaches. Our findings highlight that combining a strong generative prior with the underlying physics of image formation substantially improves reconstruction quality, e.g., 7.5% improvement on SSIM compared to full training methods. Code will be released at https://github.com/batmanlab/PhyDiCT.

Weicheng Dai, Shantanu Ghosh, Kayhan Batmanghelich

Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA

Sparse-View CT Reconstruction 3D Medical Imaging Diffusion-Based Inverse Problems Physics-Informed Diffusion Models

Oct 5, 2026stat.ML

Direct Intermediate Initialization for Tilted Diffusion Samplers

Some diffusion posterior samplers construct Gaussian-tilted intermediate distributions along the reverse process. We observe that these targets can be pulled back to clean-space posteriors with weaker conditioning, with samples transported analytically to the corresponding noisy-space target through a Gaussian bridge. For the sequential Monte Carlo (SMC) sampler MCGDiff, the effective observation variance of this pulled-back problem is up to twice the diffusion-noise variance. We exploit this structure to initialize MCGDiff directly at an intermediate time: an approximate solver samples the softened clean-space posterior, the Gaussian bridge maps these samples to the tilted target, and only the remaining SMC suffix is run. This trades asymptotic consistency for finite-particle performance. With moment-matching posterior sampling (MMPS) as the solver, the hybrid improves sliced Wasserstein distance by roughly

2\times

at matched particle count on a structured Gaussian-mixture inverse problem, and by more than an order of magnitude when the posterior-relevant mode is rare under the prior. A prior-initialization control, which retains the bridge but drops the clean-space conditioning, shows that on MCGDiff's standard Gaussian-mixture benchmark most of the improvement is insensitive to the conditioning. Conditioning the initialization gives a further consistent gain on the structured problem, and becomes decisive on a rare-mode problem, where resampling cannot repopulate a mode absent from the initial population.

Gregory D. Bellchambers

PhysicsX Ltd. London, EC2A 4DQ

Posterior Sampling Diffusion-Based Inverse Problems Diffusion Posterior Sampling

Oct 5, 2026cs.CV

Frequency-Decoupled Diffusion Guidance for Non-Blind Image Deblurring

Pretrained diffusion models provide powerful image priors for training-free posterior sampling in image restoration. To guide this sampling process, frequency-aware methods progressively incorporate measurement information across frequency bands, facilitating coarse-to-fine reconstruction. However, existing methods typically do not explicitly separate frequency activation from degradation-induced attenuation, leaving attenuation differences among inactive frequencies insufficiently modeled. In this work, we propose frequency-decoupled posterior guidance to separate frequency activation from attenuation-aware spectral regularization. Specifically, a progressive low-to-high frequency schedule determines the active measurement band, while a kernel-derived attenuation map defines a selective spectral prior over inactive components. To stabilize the sampling process, we also introduce a local trajectory regularizer that suppresses spatially irregular state-to-clean deviations. For a fixed endpoint energy, we provide a KL-regularized path-space interpretation. In practice, we construct time-dependent guidance through local energy corrections using a Tweedie plug-in approximation. Experiments on natural-image benchmarks demonstrate strong PSNR and SSIM performance across challenging non-blind deblurring settings, even at higher measurement noise levels.

Sihan Wang, Jinshu Huang, Haibin Su +1

School of Mathematical Sciences, Nankai University, Tianjin, China. · Yau Mathematical Sciences Center, Tsinghua University, Beijing, China.

Image Deblurring Frequency-Domain Image Processing Diffusion-Based Inverse Problems Diffusion Posterior Sampling

Oct 4, 2026cs.LG

Robust Ensemble Guidance for Scientific Inverse Problems

Ensemble guidance combines pretrained diffusion priors with black-box forward models to solve inverse problems without differentiating through the physical simulator. However, observation coordinates with large predictive spread or extreme residuals can dominate the ensemble correction, degrading reconstruction accuracy. We show that two simple modifications, weighting and clipping, substantially improve this correction. Our method, Robust Ensemble Guidance (REG), uses ensemble predictive spread to balance observation scales and adaptively clips standardized residuals to limit the influence of extreme discrepancies. Both operations reuse existing particles and forward predictions, requiring no additional denoiser or forward-model evaluations. Under a local linear Gaussian model, we derive conditions for reduced one-step estimation risk, bound the influence of individual observation coordinates, and characterize when these benefits persist with finite ensembles. Experiments on Navier-Stokes inversion, black-hole imaging, and acoustic full-waveform inversion demonstrate improved reconstruction over the underlying ensemble solver. In particular, REG increases black-hole reconstruction PSNR by 6.2-8.2 dB across three observation regimes and reduces Navier-Stokes reconstruction error by 26.4% in a matched-budget comparison. These findings highlight the importance of observation heterogeneity and residual influence in designing reliable generative solvers for scientific inverse problems.

Zixiang Li, Wei Wang, Yunchao Wei +2

Beijing Jiaotong University · Tsinghua University

Diffusion Model Guidance Diffusion-Based Inverse Problems PDE Inverse Problems Inverse Problems Robust Estimation

Oct 1, 2026cs.CV

PhysDEM: Physics-Defined Energy-Matching Diffusion for Spatiotemporal Field Generation under Scarce Measurements

Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a distribution over complete fields. This limits conventional data-driven diffusion models that rely on full-field datasets. We introduce PhysDEM, a physics-defined diffusion framework that combines governing equations with spatially sparse observations to generate multiple plausible fields. First, we construct a Gibbs target by reweighting a measurement-conditioned Gaussian reference with PDE residual energy. Second, we derive an exact conditional-mean identity that reduces denoising to supervised learning of the standardized energy-induced mean correction. Third, a physics-displacement probability flow cancels Gaussian reference terms and enables amortized sampling with changing measurements through Gaussian conditioning, without retraining. Experiments on synthetic PDE systems and real-world-informed applications demonstrate that PhysDEM supports coherent field recovery and efficient sampling while maintaining stable diagnostics under tested noise levels, illustrating its practical value for field assessment. To our knowledge, PhysDEM is the first physics-defined diffusion model enabling amortized spatiotemporal field inference without preassembled full-field datasets.

Zhenyu Liang, Yining Huang, Yubo Zhao +1

HKUST · UT Austin

Physics-Informed Diffusion Models Physics-Informed Generative Modeling Diffusion Model Sampling Physics-Informed ML Diffusion-Based Inverse Problems PDE Inverse Problems

Oct 1, 2026cs.LG

Learned End-to-End Guidance Schedules for Diffusion Models

Diffusion models are a powerful generative paradigm used across multimedia and scientific applications. Guided diffusion methods impose requirements on the generation by adding the gradient of a differentiable loss (the guidance function) as a drift term during inference. The weight of this drift (the guidance scale) is critical for the trade-off between data quality and requirement satisfaction. To achieve both of these goals, guided diffusion must resort to small guidance scales and lengthy sampling, incurring high computational costs. This work proposes learned end-to-end guidance schedules (LEEGS) to achieve these objectives with fewer sampling steps. LEEGS trains a time-dependent schedule by minimizing the guidance function over a small set of examples using stochastic gradient descent. Backpropagating through guided sampling is computationally expensive, so LEEGS uses an approximation of the gradient that cuts training time by a factor of 4. We evaluate LEEGS on diverse guidance tasks, including (a) image inpainting, (b) noisy image inverse problems, (c) face-ID-guided generation, and (d) forward and inverse PDE problems, outperforming baselines at equal budget (50 or 100 NFEs), or matching constant guidance with only 10% of the steps.

Aneesh Barthakur, Mathias Niepert, Luiz F. O. Chamon

University of Stuttgart · École polytechnique, Institut Polytechnique de Paris

Diffusion Model Guidance Few-Step Diffusion Sampling Diffusion-Based Inverse Problems

Sep 30, 2026astro-ph.SR

MAGiDiff: Sampling the Photospheric Vector Field from UV/EUV Filtergrams

Photospheric vector magnetic fields are foundational to modeling, understanding, and forecasting solar activity. These data are usually produced by inverting and disambiguating the full Stokes vector at multiple passbands, which is demanding. Here, we investigate how well we can estimate photospheric vector magnetograms from UV/EUV filtergrams. This problem is challenging and intrinsically ambiguous without polarization information, as the mapping from UV/EUV intensity to the magnetic field is indirect and ill-posed. We introduce MAGiDiff, a machine-learning-based method that uses denoising diffusion models to estimate vector magnetograms from UV/EUV filtergrams. As input, MAGiDiff takes a stack of filtergrams from the Solar Dynamics Observatory (SDO) / Atmospheric Imaging Assembly (AIA); as output, it is trained to estimate the disambiguated vector magnetogram as seen by Hinode / Solar Optical Telescope-Spectro-Polarimeter (SOT-SP). We show that MAGiDiff can accurately mimic the Hinode ground-truth. Additionally, we probe MAGiDiff's understanding of the physical structure and magnetic connectivity. On full-disk, we show that it produces plausible structures for active regions. MAGiDiff generalizes across solar cycles despite hemispheric polarity reversal, and can be fine-tuned to other EUV instruments including STEREO/EUVI and GOES-R/SUVI. While clearly not a substitute for a dedicated instrument, MAGiDiff opens the door to new capabilities.

Ruoyu Wang, David Fouhey

NYU

Image Reconstruction Diffusion-Based Inverse Problems

Sep 29, 2026cs.CV

Principled MAP estimation for inverse problems: bridging the gap between convergence and performance

Pretrained denoisers provide a powerful way to incorporate image priors into restoration algorithms. Plug-and-Play and RED approaches exploit fixed-noise-level denoisers within first-order optimization schemes, with convergence guarantees, but often struggle to achieve high-quality reconstruction on severely ill-posed inverse problems. In contrast, recent state-of-the-art approaches leverage denoisers derived from flow- or diffusion-based generative models and evaluate them along a sequence of decreasing noise levels. While these methods achieve strong empirical performance, their convergence theory remains limited. In this paper, we bridge this gap by specifically designing an algorithm that combines denoisers at decreasing noise levels with a schedule tailored to ensure convergence. From a Bayesian perspective, we prove that our method converges to a

\textit{Maximum a Posteriori}

(MAP) estimate, under suitable assumptions. Subsequently, we apply our method to various ill-posed inverse problems and show that it surpasses convergent methods while competing with state-of-the-art empirical ones.

Alexandre Lagier, Valentine Tosel, Anne Gagneux +2

ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, Inria, LIP UMR 5668, 69342 Lyon Cedex 07, France · Univ. Bordeaux, Inria, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France · Inria, ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, LIP UMR 5668, 69342 Lyon Cedex 07, France

Bayesian Inverse Problems Bayesian Inference Image Restoration Diffusion-Based Inverse Problems Image Inverse Problems

Sep 28, 2026cs.LG

Cyclostationary Phase Conditioning for Medical Time Series Diffusion

Many physiological time series, such as cardiac and brain recordings, exhibit cyclostationarity: their statistics vary periodically with an underlying cycle phase. Corruption from motion, poor contact, and physiological interference obscures morphology needed for diagnosis, making signal restoration essential. Existing diffusion approaches condition on corrupted observations alone and must learn cyclic structure implicitly. We instead propose two inductive biases which encode cyclostationarity: a shift-covariant wavelet representation and dense per-sample phase conditioning inferred from the corrupted input. We further introduce a training-free cyclostationarity index that quantifies phase structure and predicts when phase conditioning will help. Finally, we propose antithetic coupling of reverse trajectories to reduce sampling variance while achieving comparable performance with fivefold fewer network evaluations. Across modalities, our results show that explicitly encoding measurable cyclic structure improves physiological time-series restoration.

Samuel Ruiperez-Campillo, Michele Copetti, Jorge da Silva Goncalves +3

Dept. of Computer Science ETH Zurich

Time Series Imputation Diffusion-Based Inverse Problems Conditional Diffusion Models Non-Stationary Time Series

Sep 28, 2026cs.LG

GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors

Active grounding of a frozen diffusion prior requires jointly determining where new measurements should be taken and how they should be used to refine the current reconstruction. Posterior-ensemble-based methods can estimate acquisition utility from generated samples, but require repeated ensemble generation as observations accumulate and capture posterior geometry only through empirical statistics. This paper proposes GPARA, which learns a context-dependent graph surrogate over diffusion prediction residuals, inducing an explicitly reusable posterior response operator that propagates measurement innovations to unobserved variables and evaluates candidate measurements through weighted posterior-risk reduction. Under the matched surrogate, we show that the same response operator also determines expected one-step acquisition benefit and yields an analytic ranking consistent with expected reconstruction improvement. A bounded learned residual calibrates the analytic utility to account for surrogate mismatch, while a small prior ensemble is generated once and reconditioned to update risk weights without repeated diffusion posterior sampling during acquisition. Experiments on two reconstruction tasks spanning physical field and computer vision show consistent improvements in refinement and active acquisition over the evaluated baselines. Ablations further support the complementary roles of step-wise graph refinement, adaptive risk weighting, and analytically anchored calibration.

Wangqian Chen, Hao Wang, Yumeng Zhang +3

The Hong Kong University of Science and Technology · The Chinese University of Hong Kong, Shenzhen

Surrogate Modeling Active Sensing Diffusion-Based Inverse Problems Diffusion Models

Sep 27, 2026cs.CV

CLIMB-flow: Coupled Linear Inverse posterior sampling via Multiscale-Based flow

Diffusion models are now widely used in Bayesian inverse problems in imaging as priors, where latent diffusion models are often used for larger scale problems to keep the computational complexity and model-size manageable. Unfortunately, the auto-encoder based compression results in loss of spatial detail. In addition, the optimization is converted to a non-linear problem. In this paper, we introduce a posterior sampling algorithm customized for the pyramidal/cascaded architecture, which relies on a coarse to fine hierarchical strategy to generate images in the pixel domain. We present CLIMB-Flow which alternates between three steps: an end-point estimation from the current coarse and noisy image, data-consistent update of the clean image, and re-noising it back to the level the network expects. Together these steps sample the posterior at that scale using an approximate Gibbs sampling from two conditional distributions. Experiments on ImageNet, CelebA, AFHQ and fastMRI span inpainting, deblurring, super-resolution and accelerated MRI, with PSNR gains of 1.37-7.66 dB over the strongest competing method on CelebA and pixel-domain reconstruction up to 512x512.

Zeqiu Yu, Ruizhi Yuan, Mathews Jacob

Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, USA · Department of Biostatistics and Health Data Science, University of Pittsburgh, Pittsburgh, PA, USA

Diffusion Models for Image Restoration Diffusion Sampling Pixel-Space Diffusion Models Diffusion-Based Inverse Problems Diffusion Posterior Sampling

Sep 24, 2026cs.LG

FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference

Diffusion models are powerful priors for linear inverse problems, but the reference guidance methods, Diffusion Posterior Sampling (DPS) and Pseudoinverse-Guided Diffusion Models (

Π

GDM), rely on scalar hyperparameters tuned per task, usually against the ground truth. We introduce FB-GDM, a fully-Bayesian guided diffusion method that removes this calibration step. Starting from the Gaussian approximation of

Π

GDM, we derive a closed-form conditional score that depends on two precision parameters (inverse variances), one associated with the denoising approximation and one with the observation likelihood, and treat them as latent variables inferred by variational inference at each reverse step. A separable factorization makes each update scale linearly with the number of pixels, so the inference stays tractable at full image resolution, at a cost comparable to one

Π

GDM run. FB-GDM requires neither the noise level nor the ground truth: its only inputs are the observation and the forward operator. Experiments on CelebA-HQ inverse problems establish two results. (i) The precision parameters, inferred from the observation alone, allow FB-GDM to outperform

Π

GDM at its nominal setting, even when the latter is given the true noise level, by up to 14 dB depending on the operator, and to match the ground-truth-calibrated

Π

GDM oracle within 0.1 dB. (ii) FB-GDM is robust when the forward operator, the noise level, or the image distribution changes: it stays close to a per-problem

Π

GDM oracle throughout and does not exhibit the hallucinations observed with DPS, whereas DPS substantially degrades at a fixed scale and

Π

GDM stays competitive only if it is re-tuned against the ground truth for each new problem. When the prior is applied to images outside its training set, this re-balancing between data and prior keeps FB-GDM faithful where a fixed face-prior guidance can otherwise hallucinate.

Gatien Séguy, Thomas Rodet

SATIE · SATIE Laboratory, ENS Paris-Saclay, CNRS, Universit´e Paris-Saclay, 91190 Gif-sur-Yvette, France

Diffusion Model Guidance Bayesian Inverse Problems Diffusion-Based Inverse Problems Inverse Problems

Sep 21, 2026cs.AI

Unsupervised Brain Anomaly Detection as a Bayesian Inverse Problem with Diffusion Prior

Unsupervised anomaly detection (UAD) aims to localize abnormal regions in medical scans without pixel-level annotations. A typical strategy seeks to reconstruct a pseudo-healthy image that preserves subject-specific anatomy. Recently, diffusion models have been proposed to perform UAD. However, these methods rely on heuristic noise schedules or synthetic corruptions to balance subject-specificity and anomaly removal. In this work, we propose an alternative formulation of UAD as a Bayesian inverse problem under a diffusion prior. First, we introduce a latent spatial anomaly mask that models pixel-wise consistency between a test image and its latent corresponding pseudo-healthy image. Then, we propose an approximation of the unknown generation process that links healthy anatomy, anomalies, and the observed image, enabling a well-defined likelihood within the Bayesian framework. Building on recent advances in diffusion-based inverse problem methods, we jointly infer the pseudo-healthy image and the anomaly mask via annealed posterior sampling. We evaluate our approach on FDG PET (ADNI) and FLAIR MRI (BraTS 2021), demonstrating improved anomaly localization performance compared to other diffusion-based approaches and validating the contribution of our introduced model. Our code is available at https://github.com/HuguesRoy/UAD_DAPS.

Hugues Roy, Reuben Dorent, Ninon Burgos

Sorbonne Université, Institut du Cerveau - Paris Brain Institute - ICM, CNRS, Inria, Inserm, AP-HP, Hôpital de la Pitié Salpêtrière, F-75013, Paris, France

Medical Image Anomaly Detection Anomaly Localization Reconstruction-Based Anomaly Detection Unsupervised Anomaly Detection Diffusion-Based Inverse Problems

Sep 17, 2026cs.CV

STAR: Structure-aware Test-time Adaptation for diffusion-based light field Reconstruction

Light field (LF) reconstruction from limited and noisy focal stack (FS) measurements is a highly ill-posed inverse problem. Although the LF-to-FS imaging geometry is fixed for a given optical setup, LF spatial-angular structure---including within-view spatial details, cross-view angular dependencies, and disparity across views---varies across scenes. Consequently, a fixed pre-trained prior may not optimally capture the spatial-angular structure of each test LF. We propose Structure-aware Test-time Adaptation for diffusion-based light field Reconstruction (STAR), the first test-time adaptation framework for reconstructing an LF from FS. For each test LF, STAR freezes a pre-trained diffusion prior and fits three lightweight adapters to the observed FS to jointly adapt the three components of the LF's spatial-angular structure. STAR outperforms existing state-of-the-art methods in both two- and three-focal-sheet settings, with shorter inference times than those with test-time parameter updates.

Wontae Choi, Ki Ryum Moon, Jae Young Lee +2

Department of Artificial Intelligence (AI), Sungkyunkwan University (SKKU), Suwon, South Korea · Department of Electrical and Computer Engineering, SKKU, Suwon, South Korea

Image Reconstruction Computational Imaging Diffusion-Based Inverse Problems Diffusion Models Image Inverse Problems

Sep 14, 2026cs.LG

Backward SDEs-based Diffusion for Physics-Constrained Generation

Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent projections, or task-specific conditional training, with limited guarantees of feasibility at the end of inference. We propose terminal-conditioned inversion for score-based SDE priors. Given a frozen Score-SDE prior and a task-defined terminal feasibility specification, we construct an associated backward stochastic differential equation whose adapted solution defines a principled inverse map from the terminal requirement to a prior state at a chosen noise level. Under standard regularity conditions, we establish existence and uniqueness of the adapted solution and obtain terminal consistency by construction. We further develop a practical neural BSDE solver that composes arbitrary pretrained diffusion priors with domain constraints without modifying the score-defined coefficients, producing an anchored prior state that enables neighborhood sampling for uncertainty characterization. Experiments on toy datasets validate stable terminal-conditioned inversion and distributionally consistent neighborhood sampling. As a real-world case study, we apply the framework to sparse-view CT reconstruction and achieve improved reconstruction quality over representative training-free baselines while satisfying strict measurement feasibility under the prescribed terminal specification. Project is available in: https://laplace.center/icmlbsdeI/

Zihao Wang

Diffusion Model Inversion Constrained Generative Modeling Stochastic Differential Equations Diffusion-Based Inverse Problems Image Inverse Problems

Sep 14, 2026cs.LG

Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion

Full waveform inversion (FWI) estimates subsurface velocity from seismic recordings, but its ill-posedness and nonlinearity make accurate reconstruction strongly dependent on initialization and prior information. Diffusion posterior sampling provides a learned geological prior, yet directly coupling its denoiser to the nonlinear wave solver can yield unreliable physical guidance. We propose Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity to the diffusion prior through a Gaussian bridge. The physical state is refined by waveform fitting regularized by the denoised velocity, and in turn guides the reverse diffusion process. This formulation separates the wave-equation and denoiser gradients while preserving conventional FWI initialization and accumulated optimization history. On four OpenFWI families, PSG's terminal denoised estimates outperform classical and diffusion-based baselines under clean and missing-trace acquisitions and maintain strong structural recovery under measurement noise. Repeated stochastic runs preserve the dominant geological structures, with ensemble variability concentrated near geological interfaces and positively associated with local inversion error. A frozen OpenFWI-trained prior further supports inversion of the larger Marmousi, Overthrust, and BP2004 Salt models, recovering complex geological structures without retraining.

Chen Min, Haowen Jiang, Zheng Ma +1

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China · CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, China · School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

Physics-Informed Diffusion Models Diffusion-Based Inverse Problems Diffusion Posterior Sampling PDE Inverse Problems Inverse Problems Image Inverse Problems

Sep 14, 2026cs.CV

RAIN: Region-Aware Inversion Network for Semantic Watermark Extraction

Semantic watermarks for diffusion models embed ownership information into the generative process while preserving perceptual quality, but Gaussian-Shading extraction conventionally requires multi-step diffusion inversion to recover the initial noise. Recent one-step methods show that this cost can be reduced substantially. We study this problem through extended flow matching and conditional regression. The key observation is that, near the high-SNR image endpoint, recovering a useful noise statistic given by the first-step output of the extended flow matching in the high-SNR regime is much simpler than reconstructing the full inverse trajectory, and Gaussian Shading only requires the recovered latent to remain in the correct watermark decision region. Based on this observation, we propose a lightweight, prompt-free extractor that decomposes endpoint recovery into an image-like anchor and a noise-oriented residual, which increases the capability of the model to utilize GPU parallel computation. The resulting method avoids iterative inversion and repeated evaluation of a diffusion-scale U-Net, providing an efficient one-step extraction pipeline with a concise theoretical interpretation. The computational cost of extracting noise is lower than that of both OSI and FARI. The github repo is there: https://github.com/TheLovesOfLadyPurple/RAIN-lightweight-NN-for-one-step-semantic-watermark-extraction

Zilai Li

Independent Researcher

Diffusion Model Inversion Diffusion Model Watermarking Diffusion-Based Inverse Problems

Sep 9, 2026cs.CV

Advanced Brain Tissue Imaging with Data-Consistent Diffusion Priors in Laminographic X-Ray Nanoimaging

Nanoscale imaging of mammalian brains is critical for connectomics. X-ray laminography enables high-throughput imaging of extended, plate-like biological specimens. However, the tilted acquisition geometry leads to incomplete Fourier-space coverage, giving rise to a missing-cone of information. Conventional reconstruction methods cannot recover unmeasured information within the cone, resulting in artifacts that distort fine brain structures. While resolving these requires modeling 3D structure, direct 3D deep learning approaches are limited by data scarcity and computational cost. Here we introduce LUCID (Laminography with Unified Consistent Diffusion), a framework that combines multi-view diffusion priors with projection-domain data consistency. LUCID integrates complementary 3D structural information while enforcing strict alignment with the laminography forward model. On simulated datasets, LUCID substantially improves spatial fidelity and restores missing Fourier components, outperforming baseline methods. Applied to experimental laminography data, LUCID generalizes robustly despite being trained exclusively on fully sampled tomographic volumes, and effectively recovers unmeasured Fourier information.

Wenxuan Fang, Abraham L. Levitan, Ana Diaz +10

Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland. · Paul Scherrer Institute, Villigen, Switzerland. · Sensory Circuits and Neurotechnology Lab, The Francis Crick Institute, 1 Midland Road, London, NW1 1AT, UK. +2

3D Reconstruction Image Reconstruction Diffusion-Based Inverse Problems Neuroimaging Inverse Problems

Sep 1, 2026cs.CV

Diffusion Based Unpaired Data Learning for Inverse Problems

Data is important in many deep learning-based inverse problem solvers. However, obtaining sufficient paired data in many scenarios remains highly challenging, while unpaired data is cheap. To maximize data utilization, this paper proposes LUD-DIF, a diffusion-based approach for solving inverse problems with unpaired data. Starting from the evidence lower bound (ELBO) of the joint distribution, we decouple it into two independent diffusion processes under the weak-coupling assumption. The method provides theoretical support from a variational inference perspective, derives the loss function, quantitatively analyzes the error bound introduced by the assumption, and offers a theorem-motivated heuristic for hyperparameter selection. Experimental results demonstrate that LUD-DIF achieves outstanding performance on multiple image inverse problems, validating its effectiveness and generalization capability in unpaired inverse problem settings.

Chenglong Bao, Yiming Dang, Chenguang Duan +2

Yau Mathematical Sciences Center, Tsinghua University, Beijing, China · Department of Mathematical Sciences, Tsinghua University, Beijing, China · Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany +2

Diffusion-Based Inverse Problems Inverse Problems Diffusion Models Image Inverse Problems

Aug 30, 2026cs.CV

Null-Space Diffusion Restoration with Adaptive Uncertainty-Guided Fusion for Ultrasound Speckle Reduction

Ultrasound B-mode imaging commonly suffers from speckle noise and artifacts, requiring a delicate balance between contrast, resolution, and preservation of anatomical structures. Although recently developed despeckling methods have achieved some progress, supervised learning approaches remain fundamentally limited by the ground truth paradox, which arises from the absence of noise-free, ground truth reference images in in vivo scenarios. Existing unsupervised diffusion-based methods typically enforce data consistency directly in the nonlinear log-compressed domain, which can disproportionately amplify background artifacts when mapped back to the envelope domain. To overcome these limitations, we propose an uncertainty-guided null-space diffusion (UGNS) framework, a novel label-free solution that enforces consistency correction on a stabilized positive-envelope proxy obtained via inverse log compression. The proposed UGNS introduces several technical novelties: (a) extraction of a structural prior in the stabilized envelope domain to produce a robust signal envelope that preserves anatomical structure, (b) development of an adaptive range-null reconstruction mechanism that uses an adaptive weight mask to preserve tissue regions via range-space projection, and (c) introduction of uncertainty-guided fusion in an adaptive way to mitigate sampling variability. Extensive and comparative experiments were conducted using the PICMUS benchmark and in vivo datasets. The results demonstrate that UGNS achieves competitive generalized contrast-to-noise ratio (gCNR) values across diverse datasets. In addition, it is successfully validated that UGNS effectively suppresses speckle noise while preserving fine spatial resolution. Code is available at https://github.com/yousirong/UGNS.git.

Juneyong Lee, Jaeyoung Choi

Department of Computer Science and Engineering, Hankuk University of Foreign Studies, Yongin-si 17035, Republic of Korea

Diffusion Models for Image Restoration Ultrasound Imaging Diffusion-Based Inverse Problems Diffusion Models Image Denoising

Aug 15, 2026stat.ML

A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors

Pretrained diffusion models represent image distributions through a continuum of progressively smoothed distributions. This multiscale structure organizes generation from global structure to fine detail and supports high-quality, diverse samples. We exploit the same multiscale diffusion prior for linear imaging inverse problems. Rather than using the pretrained model only as a denoiser in an outer iteration, we define a surrogate likelihood whose center is aligned with the clean-image coordinate and whose covariance accounts for residual diffusion uncertainty. This construction defines an explicit surrogate posterior path, from which we derive continuous posterior dynamics. A tunable Langevin component supports target tracking and allows the amount of posterior exploration to be adapted to the application. We prove endpoint consistency and a finite-horizon tracking bound and, in the exact-score setting, first-order weak accuracy. For computation, we derive the Posterior-Dynamics Implicit--Explicit sampler (PD-IMEX), a stable method using one score evaluation per diffusion scale and an implicit data-consistency update. Experiments on deblurring, super-resolution, and inpainting show strong reconstruction quality at 100 score evaluations, coarse-grid stability, and controllable fidelity--diversity behavior.

Zhaoqiang Liu, Tongyao Pang, Ruibing Wang +1

School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China · Yau Mathematical Sciences Center, Shuangqing Complex, Tsinghua University, Beijing 100084, China

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

Aug 9, 2026cs.CV

MRI super-resolution in ten sampling steps using a diffusion bridge model

Objective. MRI provides excellent soft-tissue contrast, but long acquisition times can cause patient discomfort and lead to motion artifacts, forcing a trade-off between spatial resolution and scan time. Diffusion-based super-resolution (SR) reconstructs high-resolution (HR) images from low-resolution (LR) inputs, but typically needs many sampling steps and initializes from a Gaussian prior ill-suited to image restoration. We developed an efficient diffusion framework that reconstructs HR MRI directly from LR data. Approach. We propose super-resolution diffusion bridge model (SR-DBM), a super-resolution diffusion bridge model that casts SR as a stochastic transport between the LR and HR image distributions. Through a Doob's h-transform of a mean-reverting stochastic differential equation, SR-DBM pins the process to the paired HR and LR images at its endpoints, initializing reconstruction from the measured anatomy rather than from Gaussian noise. The HR image is recovered by a deterministic reverse trajectory in which a network predicts the clean image at each of only ten sampling steps. We evaluated SR-DBM on ultra-high-field 7T brain T1 MP2RAGE maps and pelvic T2-weighted prostate images against nine comparison methods using PSNR, SSIM, GMSD, and LPIPS. Main results. SR-DBM attained the highest PSNR and SSIM and the lowest GMSD on both datasets (brain: 27.66+-1.52 dB, 0.96+-0.02, 7.96+-1.86$; prostate: 27.87+-2.29 dB, 0.80+-0.05, 8.38+- 1.44), with statistically significant gains over every comparison method (two-sided Wilcoxon signed-rank test with Holm correction, p<0.05). The strongest baseline, SR-EMamba, ranked second. Qualitatively, SR-DBM produced the smallest residual errors and best preserved fine structures and lesions.

Mojtaba Safari, Hang Yu, Zach Eidex +10

Department of Radiation and Cellular Oncology, The University of Chicago, Chicago, IL, United States · Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC, United States · Department of Radiation Oncology and Winship Cancer Institute, Emory University, Atlanta, GA, United States +3

Medical Image Super-Resolution Diffusion-Based Inverse Problems Diffusion MRI Diffusion Model Acceleration Brain MRI Diffusion Models

Aug 9, 2026cs.CV

eBIRD: Event-based Intensity Image Reconstruction Using Controllable Diffusion Models

Intensity-image reconstruction from event streams remains a challenging problem due to the binary, sparse, and asynchronous nature of event data. This work proposes eBIRD, an event-guided reconstruction framework that combines a DDPM with ControlNet-based conditioning. We analyze generic and specialized diffusion learning strategies for handwritten digit (N-MNIST) and face (RGBE-Gaze) reconstruction using 33ms event windows. On N-MNIST, the general model achieves the best reconstruction quality (MSE 0.0052, SSIM 0.8982, PSNR 23.34dB), whereas the specialized model performs best on RGBE-Gaze (MSE 0.0161, SSIM 0.7605, PSNR 19.08dB). These preliminary results suggest that controllable diffusion models are a promising approach for event-guided intensity-image reconstruction, while highlighting that the preferred learning strategy depends on the reconstruction domain.

Ignacio Bugueno-Cordova, Fabian Valderrama, Rodrigo Verschae

Institute of Engineering Sciences, Universidad de OHiggins, Rancagua, Chile · The Iniciativa de Datos e Inteligencia Artificial, University of Chile, Santiago, Chile

Event-Based Vision Image Reconstruction Diffusion-Based Inverse Problems Diffusion Models

Aug 7, 2026cs.CV

Local Epistemic Uncertainty Guided Active Sampling for Plug-and-play Diffusive Image Restoration

Diffusion models have demonstrated remarkable effectiveness in image restoration tasks. However, when guiding image reconstruction, existing Diffusion Model-based Image Restoration (DMIR) methods typically rely on fixed data constraints and uniform step sizes, thereby overlooking the dynamic nature of the generative process. Such rigid designs render the models vulnerable to spatially non-uniform degradations, thus resulting in structural distortions and loss of fine details. Meanwhile, uniform step sizes introduce computational redundancy, whereas naïve step reduction strategies tend to accumulate approximation errors. To address these limitations, we propose a Local Epistemic Uncertainty Guided Active Sampling framework (LEADer). In the spatial domain, LEADer leverages pixel-wise uncertainty to dynamically modulate the prior strength within the null space, which effectively balances detail preservation and artifact suppression. In the temporal domain, it quantifies sampling stability via the uncertainty trace to enable adaptive trajectory pruning, thereby accelerating convergence. Theoretical proofs demonstrate that our framework achieves strict data consistency, while the trajectory pruning strategy admits a deterministic error bound, thereby guaranteeing stable convergence under skip sampling. Notably, our plug-and-play method can be seamlessly integrated into various DMIR baselines. Extensive experiments show that LEADer improves the performance of multiple state-of-the-art DMIR methods, while significantly reducing sampling time with negligible memory overhead. Code is available at https://github.com/JiaqiZhang-Sengoku/LEADer.

Jiaqi Zhang, Zheng Pang, Rongrong Gao +2

Jiangsu University Zhenjiang, China · Xi’an University of Technology Xi’an, China

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

Aug 4, 2026cs.SD

DDSynth-RL: Audio Synthesizer Inversion via Discrete Diffusion with Reinforcement Learning

Synthesizer inversion is challenging for two main reasons: 1) Distinct parameter configurations can produce perceptually similar sounds. 2) Parameter-space losses often fail to reflect rendered audio similarity, while the synthesizer being a non-differentiable black box prevents simple audio-domain supervision. To address the one-to-many mapping induced by the first challenge, we formulate synthesizer inversion as conditional generation over discrete synthesizer parameters and use masked discrete diffusion as the generator. This treatment additionally avoids the fixed-order assumption of autoregressive models and the continuous-relaxation mismatch of flow matching when modeling categorical synthesizer controls. To address the second challenge, we further fine-tune the model with GRPO-style audio-domain rewards computed from rendered outputs. Experiments on Dexed show that, after supervised training, the discrete diffusion model is competitive with autoregressive and flow-matching baselines, and reward-based fine-tuning further improves out-of-domain audio matching performance. Code and demos are available at: https://github.com/DDSynth-RL/DDSynthRL.

Tristan Wu, Daniel Chin, Junan Zhang +3

Computational Media and Art, The Hong Kong University of Science and Technology (Guangzhou) · New York University Shanghai · The Chinese University of Hong Kong, Shenzhen +2

Diffusion-Based Inverse Problems Diffusion Models

Jul 29, 2026cs.CV

Dual Inversion for Text-to-Image Diffusion Models: From Both Prompt and Noise Perspectives

Prompt inversion, as a typical reverse engineering technique, enables text-to-image (T2I) diffusion models to generate the desired target images without extensive prompt engineering. However, existing prompt inversion methods suffer from significant limitations: (1) gradient-based methods are unstable and uninterpretable, often resulting in generated images with severe artifacts; (2) gradient-free methods yield human-readable prompts but still fail to preserve visual fidelity due to the lack of fine-grained detail alignment. We contend that the limitations stem from treating prompt inversion as a sufficient condition for reverse engineering, ignoring the critical role of the latent noise that encodes structural information. Consequently, we propose Dualin (Dual inversion), a two-stage method that jointly recovers both the semantic prompt and latent noise of the target image. In the first stage, we integrate vision-language model, CLIP and large language model to invert a faithful, human-interpretable hard prompt. In the second stage, unconditional DDIM inversion reconstructs the exact latent noise of the target image, guaranteeing the consistency at the structural information level. Theoretically, we prove that the inverted noise enables flexible image editing without re-optimization. Extensive experiments on diverse datasets demonstrate that Dualin simultaneously generates high-quality inverted prompts and achieves state-of-the-art image fidelity. Additionally, Dualin can establish a robust foundation for the precise and controllable image editing.

Xiaolong Liu, Junjian Li, Yuan Xiao +4

Geely Hangzhou, China · City University of Macau Macau, China

Diffusion Model Inversion Diffusion-Based Inverse Problems Diffusion-Based Image Editing Controllable Image Generation T2I Diffusion Models

Jul 29, 2026cs.CR

FARI: Robust One-Step Inversion for Watermarking in Diffusion Models

Inversion-based watermarking is a promising approach to authenticate diffusion-generated images, yet practical use is bottlenecked by inversion that is both slow and error-prone. While the primary challenge in the watermarking setting is robustness against external distortions, existing approaches over-optimize internal truncation error, and because that error scales with the sampler step size, they are inherently confined to high-NFE (number of function evaluations) regimes that cannot meet the dual demands of speed and robustness. In this work, we have two key observations: (i) the inversion trajectory has markedly lower curvature than the forward generation path does, making it highly compressible and amenable to low-NFE approximation; and (ii) in inversion for watermark verification, the trade-off between speed and truncation error is less critical, since external distortions dominate the error. A faster inverter provides a dual benefit: it is not only more efficient, but it also enables end-to-end adversarial training to directly target robustness, a task that is computationally prohibitive for the original, lengthy inversion trajectories. Building on this, we propose \textbf{FARI} (\textbf{F}ast \textbf{A}symmetric \textbf{R}obust \textbf{I}nversion), a one-step inversion framework paired with lightweight adversarial LoRA fine-tuning of the denoiser for watermark extraction. While consolidation slightly increases internal error, FARI delivers large gains in both speed and robustness: with approximately 20 minutes of fine-tuning on a single NVIDIA RTX A6000 GPU, it surpasses 50-step DDIM inversion on watermark-verification robustness while dramatically reducing inference time. Code and pretrained models are available at https://github.com/0xD009/FARI.

Jindong Yang, Han Fang, Weiming Zhang +2

University of Science and Technology of China · 2Anhui Province Key Laboratory of Digital Security

Diffusion Model Inversion Diffusion Model Watermarking Robust Watermarking Diffusion-Based Inverse Problems Diffusion Model Inference Acceleration Diffusion Models

Jul 28, 2026cs.CV

Noise-Free One-Step LoRA for Task-Driven Image Restoration with Diffusion Priors

Degraded images not only reduce visual quality but also impair downstream high-level vision tasks. Task-driven image restoration (TDIR) addresses this issue by jointly optimizing restoration quality and task performance. Recent works show that pretrained diffusion priors benefit TDIR, yet diffusion-based restoration is inherently stochastic, as the sampling process depends on a random noise term, which can undermine task consistency. In this paper, we show that a deterministic, noise-free one-step forward pass with pretrained diffusion priors can substantially improve TDIR, but the benefit critically depends on the adaptation module: LoRA yields consistent gains, whereas ControlNet-style conditioning does not. This enables one-step forwarding that surpasses conventional multi-step diffusion TDIR baselines. Furthermore, we introduce a task-preserving GAN training strategy that improves perceptual quality without sacrificing task performance. Extensive experiments on classification, segmentation, and detection demonstrate consistent gains over prior TDIR methods, and we further validate generalization on real-world degraded images and OCR.

Jaeha Kim, Kyoung Mu Lee

Dept. of ECE & ASRI, Seoul National University, Seoul, Korea · IPAI, Seoul National University, Seoul, Korea

Diffusion Models for Image Restoration Low-Rank Adaptation Image Restoration Diffusion-Based Inverse Problems Diffusion Model Inference Acceleration