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Andrés Almansa

Publications and source records attributed to Andrés Almansa.

At least 19 recordsLinked to original sources
arXiv2026

Iterating Consistency Models: Stability, Error Bounds and Noise Schedules

Consistency models (CMs) have become a leading approach for generating high-quality samples in few steps. However, adding steps can improve or degrade sample quality in ways that are highly sensitive to the schedule and that existing theory does not fully explain. To provide accuracy guarantees and guide CM sampler design, we analyze multistep CM sampling as a composition of noising and approximate denoising operators. Under explicit, verifiable stability assumptions, we derive a non-asymptotic error bound that separates contraction of the initialization error from accumulation of approximation error. The bound assigns distinct roles to the schedule: large early noise levels drive contraction, while small late noise levels control the residual bias. As a corollary, we obtain explicit constants for strongly log-concave and semi-log-concave targets. We further establish a complementary guarantee whose assumptions, one-step accuracy and stability, can be estimated for a given trained model. Experiments show that the contraction and approximation profiles entering our bounds can be reliably measured and closely match the predicted functional forms. Together, these results provide a meaningful convergence theory for multi-step CMs and a practical route to sampler design.

stat.ML↗
arXiv2026

BAM! Bayesian Anything Model: a foundation model for generative computational imaging

Generative models are transforming Bayesian computational imaging, yet the field still lacks physics-aware foundation models. Current practice falls into two camps. Large foundation image models are deployed as plug-and-play priors with zero-shot approximate likelihood guidance, which introduces significant bias and computational cost. Physics-aware generative models avoid this bias, but each is tied to a specific dataset, task and instrument. We introduce BAM (Bayesian Anything Model), a lightweight foundation model for few-step, physics-aware posterior sampling that generalises robustly to unseen data and tasks, zero-shot or with minimal finetuning. BAM upgrades the operator-conditioned Reconstruct Anything Model (RAM) backbone (Terris et al.) into a conditional flow map, so instrument physics is specified at inference time rather than fixed during training. BAM has just 36M parameters and is pre-trained jointly on large image corpora and libraries of forward operators. A single network then draws posterior samples in a few steps, with no likelihood approximation and no guidance weights to tune. Across linear inverse problems on FFHQ, AFHQ, LSUN, DIV2K and the Kohler camera-shake benchmark, BAM outperforms in just 3 steps both specialised models and leading zero-shot methods in sample quality, at a fraction of their computational cost. BAM gives the community an accessible entry point to generative computational imaging, lowers the economic and environmental cost of training imaging models, and opens a new path for research on physics-aware Bayesian computational imaging. Official page: https://bayesian-anything-model.github.io/

cs.CV↗
arXiv2026

Efficient Neural-Network-Based High-Resolution Radiative Transfer for CO___ Retrieval, and Application to Interferometric Sensing

Studying climate change requires reducing uncertainties in CO2 and CH4 emission estimates to better distinguish anthropogenic from natural sources, which motivates spaceborne measurements with improved revisit frequency and spatial coverage. In this context, the Horizon Europe SCARBOn project assesses a low-cost satellite constellation featuring the NanoCarb imaging interferometer as its core sensor for monitoring CO2 and CH4 emissions in the atmosphere. However, estimating CO2 and CH4 concentrations with high revisit and spatial coverage poses significant challenges: full-physics retrieval algorithms commonly used rely on repeated high-resolution radiative transfer (RT) simulations, which are computationally expensive when using line-by-line RT models. As an alternative, we propose in this study a feedforward multilayer perceptron (MLP) surrogate designed to accurately and efficiently predict top-of-atmosphere radiances in the CO2 weak band, using a combined mean absolute error (MAE) loss on radiances and RT Jacobians to preserve both spectral accuracy and sensitivity to geophysical parameters. Coupling the MLP-based RT surrogate with the NanoCarb instrumental response yields an efficient and precise forward model for NanoCarb measurements, which shows promising results for CO2 concentration retrieval.

cs.LG↗
arXiv2026

LVTINO: LAtent Video consisTency INverse sOlver for High Definition Video Restoration

Computational imaging methods increasingly rely on powerful generative diffusion models to tackle challenging image restoration tasks. In particular, state-of-the-art zero-shot image inverse solvers leverage distilled text-to-image latent diffusion models (LDMs) to achieve unprecedented accuracy and perceptual quality with high computational efficiency. However, extending these advances to high-definition video restoration remains a significant challenge, due to the need to recover fine spatial detail while capturing subtle temporal dependencies. Consequently, methods that naively apply image-based LDM priors on a frame-by-frame basis often result in temporally inconsistent reconstructions. We address this challenge by leveraging recent advances in Video Consistency Models (VCMs), which distill video latent diffusion models into fast generators that explicitly capture temporal causality. Building on this foundation, we propose LVTINO, the first zero-shot or plug-and-play inverse solver for high definition video restoration with priors encoded by VCMs. Our conditioning mechanism bypasses the need for automatic differentiation and achieves state-of-the-art video reconstruction quality with only a few neural function evaluations, while ensuring strong measurement consistency and smooth temporal transitions across frames. Extensive experiments on a diverse set of video inverse problems show significant perceptual improvements over current state-of-the-art methods that apply image LDMs frame by frame, establishing a new benchmark in both reconstruction fidelity and computational efficiency. The code is available on GitHub.

cs.CV↗
arXiv2025

Blur2seq: Blind Deblurring and Camera Trajectory Estimation from a Single Camera Motion-blurred Image

Motion blur caused by camera shake, particularly under large or rotational movements, remains a major challenge in image restoration. We propose a deep learning framework that jointly estimates the latent sharp image and the underlying camera motion trajectory from a single blurry image. Our method leverages the Projective Motion Blur Model (PMBM), implemented efficiently using a differentiable blur creation module compatible with modern networks. A neural network predicts a full 3D rotation trajectory, which guides a model-based restoration network trained end-to-end. This modular architecture provides interpretability by revealing the camera motion that produced the blur. Moreover, this trajectory enables the reconstruction of the sequence of sharp images that generated the observed blurry image. To further refine results, we optimize the trajectory post-inference via a reblur loss, improving consistency between the blurry input and the restored output. Extensive experiments show that our method achieves state-of-the-art performance on both synthetic and real datasets, particularly in cases with severe or spatially variant blur, where end-to-end deblurring networks struggle. Code and trained models are available at https://github.com/GuillermoCarbajal/Blur2Seq/

cs.CV↗
arXiv2025

LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization

Text-to-image latent diffusion models (LDMs) have recently emerged as powerful generative models with great potential for solving inverse problems in imaging. However, leveraging such models in a Plug & Play (PnP), zero-shot manner remains challenging because it requires identifying a suitable text prompt for the unknown image of interest. Also, existing text-to-image PnP approaches are highly computationally expensive. We herein address these challenges by proposing a novel PnP inference paradigm specifically designed for embedding generative models within stochastic inverse solvers, with special attention to Latent Consistency Models (LCMs), which distill LDMs into fast generators. We leverage our framework to propose LAtent consisTency INverse sOlver (LATINO), the first zero-shot PnP framework to solve inverse problems with priors encoded by LCMs. Our conditioning mechanism avoids automatic differentiation and reaches SOTA quality in as little as 8 neural function evaluations. As a result, LATINO delivers remarkably accurate solutions and is significantly more memory and computationally efficient than previous approaches. We then embed LATINO within an empirical Bayesian framework that automatically calibrates the text prompt from the observed measurements by marginal maximum likelihood estimation. Extensive experiments show that prompt self-calibration greatly improves estimation, allowing LATINO with PRompt Optimization to define new SOTAs in image reconstruction quality and computational efficiency. The code is available at https://latino-pro.github.io

cs.CV↗
arXiv2025

Infusion: internal diffusion for inpainting of dynamic textures and complex motion

Video inpainting is the task of filling a region in a video in a visually convincing manner. It is very challenging due to the high dimensionality of the data and the temporal consistency required for obtaining convincing results. Recently, diffusion models have shown impressive results in modeling complex data distributions, including images and videos. Such models remain nonetheless very expensive to train and to perform inference with, which strongly reduce their applicability to videos, and yields unreasonable computational loads. We show that in the case of video inpainting, thanks to the highly auto-similar nature of videos, the training data of a diffusion model can be restricted to the input video and still produce very satisfying results. With this internal learning approach, where the training data is limited to a single video, our lightweight models perform very well with only half a million parameters, in contrast to the very large networks with billions of parameters typically found in the literature. We also introduce a new method for efficient training and inference of diffusion models in the context of internal learning, by splitting the diffusion process into different learning intervals corresponding to different noise levels of the diffusion process. We show qualitative and quantitative results, demonstrating that our method reaches or exceeds state of the art performance in the case of dynamic textures and complex dynamic backgrounds

cs.CV↗
arXiv2025

Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

stat.ML↗
arXiv2024

Diffusion-based image inpainting with internal learning

Diffusion models are now the undisputed state-of-the-art for image generation and image restoration. However, they require large amounts of computational power for training and inference. In this paper, we propose lightweight diffusion models for image inpainting that can be trained on a single image, or a few images. We show that our approach competes with large state-of-the-art models in specific cases. We also show that training a model on a single image is particularly relevant for image acquisition modality that differ from the RGB images of standard learning databases. We show results in three different contexts: texture images, line drawing images, and materials BRDF, for which we achieve state-of-the-art results in terms of realism, with a computational load that is greatly reduced compared to concurrent methods.

cs.CV↗
arXiv2024

Diverse super-resolution with pretrained deep hiererarchical VAEs

We investigate the problem of producing diverse solutions to an image super-resolution problem. From a probabilistic perspective, this can be done by sampling from the posterior distribution of an inverse problem, which requires the definition of a prior distribution on the high-resolution images. In this work, we propose to use a pretrained hierarchical variational autoencoder (HVAE) as a prior. We train a lightweight stochastic encoder to encode low-resolution images in the latent space of a pretrained HVAE. At inference, we combine the low-resolution encoder and the pretrained generative model to super-resolve an image. We demonstrate on the task of face super-resolution that our method provides an advantageous trade-off between the computational efficiency of conditional normalizing flows techniques and the sample quality of diffusion based methods.

cs.CV↗
arXiv2023

Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution

Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the degradation model such as blur kernel. In particular, we designed an algorithm based on the well-known Expectation-Minimization (EM) estimation method and diffusion models. Our method alternates between approximating the expected log-likelihood of the inverse problem using samples drawn from a diffusion model and a maximization step to estimate unknown model parameters. For the maximization step, we also introduce a novel blur kernel regularization based on a Plug \& Play denoiser. Diffusion models are long to run, thus we provide a fast version of our algorithm. Extensive experiments on blind image deblurring demonstrate the effectiveness of our method when compared to other state-of-the-art approaches.

cs.CV↗
arXiv2023

Patch-Based Stochastic Attention for Image Editing

Attention mechanisms have become of crucial importance in deep learning in recent years. These non-local operations, which are similar to traditional patch-based methods in image processing, complement local convolutions. However, computing the full attention matrix is an expensive step with heavy memory and computational loads. These limitations curb network architectures and performances, in particular for the case of high resolution images. We propose an efficient attention layer based on the stochastic algorithm PatchMatch, which is used for determining approximate nearest neighbors. We refer to our proposed layer as a "Patch-based Stochastic Attention Layer" (PSAL). Furthermore, we propose different approaches, based on patch aggregation, to ensure the differentiability of PSAL, thus allowing end-to-end training of any network containing our layer. PSAL has a small memory footprint and can therefore scale to high resolution images. It maintains this footprint without sacrificing spatial precision and globality of the nearest neighbors, which means that it can be easily inserted in any level of a deep architecture, even in shallower levels. We demonstrate the usefulness of PSAL on several image editing tasks, such as image inpainting, guided image colorization, and single-image super-resolution. Our code is available at: https://github.com/ncherel/psal

cs.CV↗
arXiv2023

Inverse problem regularization with hierarchical variational autoencoders

In this paper, we propose to regularize ill-posed inverse problems using a deep hierarchical variational autoencoder (HVAE) as an image prior. The proposed method synthesizes the advantages of i) denoiser-based Plug \& Play approaches and ii) generative model based approaches to inverse problems. First, we exploit VAE properties to design an efficient algorithm that benefits from convergence guarantees of Plug-and-Play (PnP) methods. Second, our approach is not restricted to specialized datasets and the proposed PnP-HVAE model is able to solve image restoration problems on natural images of any size. Our experiments show that the proposed PnP-HVAE method is competitive with both SOTA denoiser-based PnP approaches, and other SOTA restoration methods based on generative models.

cs.CV↗
arXiv2023

Provably Convergent Plug & Play Linearized ADMM, applied to Deblurring Spatially Varying Kernels

Plug & Play methods combine proximal algorithms with denoiser priors to solve inverse problems. These methods rely on the computability of the proximal operator of the data fidelity term. In this paper, we propose a Plug & Play framework based on linearized ADMM that allows us to bypass the computation of intractable proximal operators. We demonstrate the convergence of the algorithm and provide results on restoration tasks such as super-resolution and deblurring with non-uniform blur.

cs.CV↗
arXiv2022

Deep Model-Based Super-Resolution with Non-uniform Blur

We propose a state-of-the-art method for super-resolution with non-uniform blur. Single-image super-resolution methods seek to restore a high-resolution image from blurred, subsampled, and noisy measurements. Despite their impressive performance, existing techniques usually assume a uniform blur kernel. Hence, these techniques do not generalize well to the more general case of non-uniform blur. Instead, in this paper, we address the more realistic and computationally challenging case of spatially-varying blur. To this end, we first propose a fast deep plug-and-play algorithm, based on linearized ADMM splitting techniques, which can solve the super-resolution problem with spatially-varying blur. Second, we unfold our iterative algorithm into a single network and train it end-to-end. In this way, we overcome the intricacy of manually tuning the parameters involved in the optimization scheme. Our algorithm presents remarkable performance and generalizes well after a single training to a large family of spatially-varying blur kernels, noise levels and scale factors.

cs.CV↗
arXiv2022

Video Restoration with a Deep Plug-and-Play Prior

This paper presents a novel method for restoring digital videos via a Deep Plug-and-Play (PnP) approach. Under a Bayesian formalism, the method consists in using a deep convolutional denoising network in place of the proximal operator of the prior in an alternating optimization scheme. We distinguish ourselves from prior PnP work by directly applying that method to restore a digital video from a degraded video observation. This way, a network trained once for denoising can be repurposed for other video restoration tasks. Our experiments in video deblurring, super-resolution, and interpolation of random missing pixels all show a clear benefit to using a network specifically designed for video denoising, as it yields better restoration performance and better temporal stability than a single image network with similar denoising performance using the same PnP formulation. Moreover, our method compares favorably to applying a different state-of-the-art PnP scheme separately on each frame of the sequence. This opens new perspectives in the field of video restoration.

eess.IV↗
arXiv2022

Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior

In this work we address the problem of solving ill-posed inverse problems in imaging where the prior is a variational autoencoder (VAE). Specifically we consider the decoupled case where the prior is trained once and can be reused for many different log-concave degradation models without retraining. Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations. The resulting technique (JPMAP) performs Joint Posterior Maximization using an Autoencoding Prior. We show theoretical and experimental evidence that the proposed objective function is quite close to bi-convex. Indeed it satisfies a weak bi-convexity property which is sufficient to guarantee that our optimization scheme converges to a stationary point. We also highlight the importance of correctly training the VAE using a denoising criterion, in order to ensure that the encoder generalizes well to out-of-distribution images, without affecting the quality of the generative model. This simple modification is key to providing robustness to the whole procedure. Finally we show how our joint MAP methodology relates to more common MAP approaches, and we propose a continuation scheme that makes use of our JPMAP algorithm to provide more robust MAP estimates. Experimental results also show the higher quality of the solutions obtained by our JPMAP approach with respect to other non-convex MAP approaches which more often get stuck in spurious local optima.

stat.ML↗
arXiv2022

On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent

Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the literature, from simple ones expressing local properties to more involved ones exploiting image redundancy at a non-local scale. In a departure from explicit modelling, several recent works have proposed and studied the use of implicit priors defined by an image denoising algorithm. This approach, commonly known as Plug & Play (PnP) regularisation, can deliver remarkably accurate results, particularly when combined with state-of-the-art denoisers based on convolutional neural networks. However, the theoretical analysis of PnP Bayesian models and algorithms is difficult and works on the topic often rely on unrealistic assumptions on the properties of the image denoiser. This papers studies maximum-a-posteriori (MAP) estimation for Bayesian models with PnP priors. We first consider questions related to existence, stability and well-posedness, and then present a convergence proof for MAP computation by PnP stochastic gradient descent (PnP-SGD) under realistic assumptions on the denoiser used. We report a range of imaging experiments demonstrating PnP-SGD as well as comparisons with other PnP schemes.

stat.ML↗