arXiv subjects

Ulugbek S. Kamilov

Publications and source records attributed to Ulugbek S. Kamilov.

At least 19 recordsLinked to original sources

arXiv2026

SNaP: One-Step Posterior Sampling for Noisy Inverse Problems

Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250 $\times$ faster than iterative samplers.

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arXiv2026

FIRM: Flow-based Imaging via Regularized Minimization

Flow matching methods for imaging inverse problems typically incorporate measurements through network conditioning or guidance during sampling. Neither approach explicitly applies the forward operator within the learned conditional velocity field. We develop a principled measurement-conditional velocity parameterization that does. For a linear interpolation path, we express the optimal velocity through the posterior mean $E[x_1|x_t, y]$ and show that this mean is the unique minimizer of a variational objective with an explicit data-consistency term. The velocity defined by this minimizer provably transports the source distribution to the measurement-conditioned posterior. This result leads to a forward operator-aware velocity field that is trained end-to-end and requires no separate guidance during sampling. Across five imaging tasks, our method achieves leading reconstruction quality with up to $50\times$ fewer network evaluations than competitive flow-based methods. Varying the number of sampling steps also controls the distortion-perception trade-off without retraining.

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arXiv2026

Next-Dense-Stride Prediction for Multimodal Autoregressive Visual Modeling

We introduce DenseAR, a new generative paradigm that reformulates autoregressive image generation as coarse-to-fine next-dense-stride prediction using a compact single-scale tokenizer. Our key insight is that traversing a single-scale latent grid with progressively denser strides naturally captures the transition from global structure to fine detail. This addresses two limitations of existing autoregressive models at once: the slow inference of raster-order autoregression, which DenseAR avoids by predicting multiple tokens in parallel, and the heavy cost of multi-scale approaches, which need long, multi-resolution token sequences to achieve coarse-to-fine prediction. Building on our efficient framework and the flexibility of autoregressive modeling, we further extend DenseAR to a unified model that handles multiple modalities and imaging tasks within a single backbone. We validate DenseAR on both medical and natural images. On multi-contrast brain MRI, a single DenseAR model unifies cross-modal translation, modality-conditioned generation, and tumor segmentation, while remaining competitive with task-specific methods. On ImageNet, DenseAR improves class-conditional generation quality (FID and IS) over both a single-grid baseline without stride ordering and a multi-scale tokenizer-based baseline.

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arXiv2026

NullFlow: One-Step Generative Reconstruction

We propose NullFlow, a principled framework for one-step generative image reconstruction. Our key idea is to confine the generative flow to a measurement-consistent subspace. Because the flow never leaves this subspace, NullFlow needs no separate data-fidelity corrections, unlike existing solvers. NullFlow samples in a single network evaluation by learning the flow's average velocity, avoiding the step-by-step integration of traditional flow matching methods. We prove that the average velocity of this constrained flow yields a training objective whose global minimizer is a one-step posterior sampler. We show on image inpainting that NullFlow matches state-of-the-art diffusion solvers while cutting inference from hundreds of network evaluations to one.

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arXiv2026

Stochastic Generative Plug-and-Play Priors

Plug-and-play (PnP) methods are widely used for solving imaging inverse problems by incorporating a denoiser into optimization algorithms. Score-based diffusion models (SBDMs) have recently demonstrated strong generative performance through a denoiser trained across a wide range of noise levels. Despite their shared reliance on denoisers, it remains unclear how to systematically use SBDMs as priors within the PnP framework without relying on reverse diffusion sampling. In this paper, we establish a score-based interpretation of PnP that justifies using pretrained SBDMs directly within PnP algorithms. Building on this connection, we introduce a stochastic generative PnP (SGPnP) framework that injects noise to better leverage the expressive generative SBDM priors, thereby improving robustness in severely ill-posed inverse problems. We provide a new theory showing that this noise injection induces optimization on a Gaussian-smoothed objective and promotes escape from strict saddle points. Experiments on challenging inverse tasks, such as multi-coil MRI reconstruction and large-mask natural image inpainting, demonstrate consistent improvement over conventional PnP methods and achieve performance competitive with diffusion-based solvers.

cs.CV↗

arXiv2026

A Unified Framework for Multimodal Image Reconstruction and Synthesis using Denoising Diffusion Models

Image reconstruction and image synthesis are important for handling incomplete multimodal imaging data, but existing methods require various task-specific models, complicating training and deployment workflows. We introduce Any2all, a unified framework that addresses this limitation by formulating these disparate tasks as a single virtual inpainting problem. We train a single, unconditional diffusion model on the complete multimodal data stack. This model is then adapted at inference time to ``inpaint'' all target modalities from any combination of inputs of available clean images or noisy measurements. We validated Any2all on a PET/MR/CT brain dataset. Our results show that Any2all can achieve excellent performance on both multimodal reconstruction and synthesis tasks, consistently yielding images with competitive distortion-based performance and superior perceptual quality over specialized methods.

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arXiv2025

Deep Parameter Interpolation for Scalar Conditioning

We propose deep parameter interpolation (DPI), a general-purpose method for transforming an existing deep neural network architecture into one that accepts an additional scalar input. Recent deep generative models, including diffusion models and flow matching, employ a single neural network to learn a time- or noise level-dependent vector field. Designing a network architecture to accurately represent this vector field is challenging because the network must integrate information from two different sources: a high-dimensional vector (usually an image) and a scalar. Common approaches either encode the scalar as an additional image input or combine scalar and vector information in specific network components, which restricts architecture choices. Instead, we propose to maintain two learnable parameter sets within a single network and to introduce the scalar dependency by dynamically interpolating between the parameter sets based on the scalar value during training and sampling. DPI is a simple, architecture-agnostic method for adding scalar dependence to a neural network. We demonstrate that our method improves denoising performance and enhances sample quality for both diffusion and flow matching models, while achieving computational efficiency comparable to standard scalar conditioning techniques. Code is available at https://github.com/wustl-cig/parameter_interpolation.

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arXiv2025

Kernel Density Steering: Inference-Time Scaling via Mode Seeking for Image Restoration

Diffusion models show promise for image restoration, but existing methods often struggle with inconsistent fidelity and undesirable artifacts. To address this, we introduce Kernel Density Steering (KDS), a novel inference-time framework promoting robust, high-fidelity outputs through explicit local mode-seeking. KDS employs an $N$-particle ensemble of diffusion samples, computing patch-wise kernel density estimation gradients from their collective outputs. These gradients steer patches in each particle towards shared, higher-density regions identified within the ensemble. This collective local mode-seeking mechanism, acting as "collective wisdom", steers samples away from spurious modes prone to artifacts, arising from independent sampling or model imperfections, and towards more robust, high-fidelity structures. This allows us to obtain better quality samples at the expense of higher compute by simultaneously sampling multiple particles. As a plug-and-play framework, KDS requires no retraining or external verifiers, seamlessly integrating with various diffusion samplers. Extensive numerical validations demonstrate KDS substantially improves both quantitative and qualitative performance on challenging real-world super-resolution and image inpainting tasks.

cs.CV↗

arXiv2025

Moments Matter: Posterior Recovery in Poisson Denoising via Log-Networks

Poisson denoising plays a central role in photon-limited imaging applications such as microscopy, astronomy, and medical imaging. It is common to train deep learning models for denoising using the mean-squared error (MSE) loss, which corresponds to computing the posterior mean $\mathbb{E}[x \mid y]$. When the noise is Gaussian, Tweedie's formula enables approximation of the posterior distribution through its higher-order moments. However, this connection no longer holds for Poisson denoising: while $ \mathbb{E}[x \mid y] $ still minimizes MSE, it fails to capture posterior uncertainty. We propose a new strategy for Poisson denoising based on training a log-network. Instead of predicting the posterior mean $ \mathbb{E}[x \mid y] $, the log-network is trained to learn $\mathbb{E}[\log x \mid y]$, leveraging the logarithm as a convenient parameterization for the Poisson distribution. We provide a theoretical proof that the proposed log-network enables recovery of higher-order posterior moments and thus supports posterior approximation. Experiments on simulated data show that our method matches the denoising performance of standard MMSE models while providing access to the posterior.

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arXiv2025

EigenScore: OOD Detection using Covariance in Diffusion Models

Out-of-distribution (OOD) detection is critical for the safe deployment of machine learning systems in safety-sensitive domains. Diffusion models have recently emerged as powerful generative models, capable of capturing complex data distributions through iterative denoising. Building on this progress, recent work has explored their potential for OOD detection. We propose EigenScore, a new OOD detection method that leverages the eigenvalue spectrum of the posterior covariance induced by a diffusion model. We argue that posterior covariance provides a consistent signal of distribution shift, leading to larger trace and leading eigenvalues on OOD inputs, yielding a clear spectral signature. We further provide analysis explicitly linking posterior covariance to distribution mismatch, establishing it as a reliable signal for OOD detection. To ensure tractability, we adopt a Jacobian-free subspace iteration method to estimate the leading eigenvalues using only forward evaluations of the denoiser. Empirically, EigenScore achieves SOTA performance, with up to 5% AUROC improvement over the best baseline. Notably, it remains robust in near-OOD settings such as CIFAR-10 vs CIFAR-100, where existing diffusion-based methods often fail.

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arXiv2025

Measurement Score-Based MRI Reconstruction with Automatic Coil Sensitivity Estimation

Diffusion-based inverse problem solvers (DIS) have recently shown outstanding performance in compressed-sensing parallel MRI reconstruction by combining diffusion priors with physical measurement models. However, they typically rely on pre-calibrated coil sensitivity maps (CSMs) and ground truth images, making them often impractical: CSMs are difficult to estimate accurately under heavy undersampling and ground-truth images are often unavailable. We propose Calibration-free Measurement Score-based diffusion Model (C-MSM), a new method that eliminates these dependencies by jointly performing automatic CSM estimation and self-supervised learning of measurement scores directly from k-space data. C-MSM reconstructs images by approximating the full posterior distribution through stochastic sampling over partial measurement posterior scores, while simultaneously estimating CSMs. Experiments on the multi-coil brain fastMRI dataset show that C-MSM achieves reconstruction performance close to DIS with clean diffusion priors -- even without access to clean training data and pre-calibrated CSMs.

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arXiv2025

Analysis Plug-and-Play Methods for Imaging Inverse Problems

Plug-and-Play Priors (PnP) is a popular framework for solving imaging inverse problems by integrating learned priors in the form of denoisers trained to remove Gaussian noise from images. In standard PnP methods, the denoiser is applied directly in the image domain, serving as an implicit prior on natural images. This paper considers an alternative analysis formulation of PnP, in which the prior is imposed on a transformed representation of the image, such as its gradient. Specifically, we train a Gaussian denoiser to operate in the gradient domain, rather than on the image itself. Conceptually, this is an extension of total variation (TV) regularization to learned TV regularization. To incorporate this gradient-domain prior in image reconstruction algorithms, we develop two analysis PnP algorithms based on half-quadratic splitting (APnP-HQS) and the alternating direction method of multipliers (APnP-ADMM). We evaluate our approach on image deblurring and super-resolution, demonstrating that the analysis formulation achieves performance comparable to image-domain PnP algorithms.

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arXiv2025

Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based methods integrate data consistency steps by approximating the likelihood function within the diffusion reverse sampling process. In this paper, we show that the existing approximations are either insufficient or computationally inefficient. To address these issues, we propose a unified likelihood approximation method that incorporates a covariance correction term to enhance the performance and avoids propagating gradients through the diffusion model. The correction term, when integrated into the reverse diffusion sampling process, achieves better convergence towards the true data posterior for selected distributions and improves performance on real-world natural image datasets. Furthermore, we present an efficient way to factorize and invert the covariance matrix of the likelihood function for several inverse problems. Our comprehensive experiments demonstrate the effectiveness of our method over several existing approaches. Code available at https://github.com/CSIPlab/CoDPS.

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arXiv2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. We address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

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arXiv2025

Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals -- particularly natural images -- and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.

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arXiv2025

Dose-aware Diffusion Model for 3D PET Image Denoising: Multi-institutional Validation with Reader Study and Real Low-dose Data

Reducing scan times, radiation dose, and enhancing image quality for lower-performance scanners, are critical in low-dose PET imaging. Deep learning techniques have been investigated for PET image denoising. However, existing models have often resulted in compromised image quality when achieving low-count/low-dose PET and have limited generalizability to different image noise-levels, acquisition protocols, and patient populations. Recently, diffusion models have emerged as the new state-of-the-art generative model to generate high-quality samples and have demonstrated strong potential for medical imaging tasks. However, for low-dose PET imaging, existing diffusion models failed to generate consistent 3D reconstructions, unable to generalize across varying noise-levels, often produced visually-appealing but distorted image details, and produced images with biased tracer uptake. Here, we develop DDPET-3D, a dose-aware diffusion model for 3D low-dose PET imaging to address these challenges. Collected from 4 medical centers globally with different scanners and clinical protocols, we evaluated the proposed model using a total of 9,783 18F-FDG studies with low-dose levels ranging from 1% to 50%. With a cross-center, cross-scanner validation, the proposed DDPET-3D demonstrated its potential to generalize to different low-dose levels, different scanners, and different clinical protocols. As confirmed with reader studies performed by board-certified nuclear medicine physicians, experienced readers judged the images to be similar or superior to the full-dose images and previous DL baselines based on qualitative visual impression. Lesion-level quantitative accuracy was evaluated using a Monte Carlo simulation study and a lesion segmentation network. The presented results show the potential to achieve low-dose PET while maintaining image quality. Real low-dose scans was also included for evaluation.

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arXiv2025

FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems

Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used frameworks such as Plug-and-Play (PnP) algorithms. In this work, we introduce Fixed-points of Restoration (FiRe) priors as a new framework for expanding the notion of priors in PnP to general restoration models beyond traditional denoising models. The key insight behind FiRe is that smooth images emerge as fixed points of the composition of a degradation operator with the corresponding restoration model. This enables us to derive an explicit formula for our implicit prior by quantifying invariance of images under this composite operation. Adopting this fixed-point perspective, we show how various restoration networks can effectively serve as priors for solving inverse problems. The FiRe framework further enables ensemble-like combinations of multiple restoration models as well as acquisition-informed restoration networks, all within a unified optimization approach. Experimental results validate the effectiveness of FiRe across various inverse problems, establishing a new paradigm for incorporating pretrained restoration models into PnP-like algorithms. Code available at https://github.com/matthieutrs/fire.

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arXiv2025

Plug-and-Play Posterior Sampling for Blind Inverse Problems

We introduce Blind Plug-and-Play Diffusion Models (Blind-PnPDM) as a novel framework for solving blind inverse problems where both the target image and the measurement operator are unknown. Unlike conventional methods that rely on explicit priors or separate parameter estimation, our approach performs posterior sampling by recasting the problem into an alternating Gaussian denoising scheme. We leverage two diffusion models as learned priors: one to capture the distribution of the target image and another to characterize the parameters of the measurement operator. This PnP integration of diffusion models ensures flexibility and ease of adaptation. Our experiments on blind image deblurring show that Blind-PnPDM outperforms state-of-the-art methods in terms of both quantitative metrics and visual fidelity. Our results highlight the effectiveness of treating blind inverse problems as a sequence of denoising subproblems while harnessing the expressive power of diffusion-based priors.

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