Zero-shot diffusion posterior sampling offers a flexible framework for inverse problems by accommodating arbitrary degradation operators at test time, but incurs high computational cost due to repeated likelihood-guided updates. In contrast, previous amortized diffusion approaches enable fast inference by replacing likelihood-based sampling with implicit inference models, but at the expense of robustness to unseen degradations. We introduce an amortization strategy for diffusion posterior sampling that preserves explicit likelihood guidance by amortizing the inner optimization problems arising in variational diffusion posterior sampling. This accelerates inference for in-distribution degradations while maintaining robustness to previously unseen operators, thereby improving the trade-off between efficiency and flexibility in diffusion-based inverse problems.

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images -- the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or misspecified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort.

Consistent improvement of image priors over the years has led to the development of better inverse problem solvers. Diffusion models are the newcomers to this arena, posing the strongest known prior to date. Recently, such models operating in a latent space have become increasingly predominant due to their efficiency. In recent works, these models have been applied to solve inverse problems. Working in the latent space typically requires multiple applications of an Autoencoder during the restoration process, which leads to both computational and restoration quality challenges. In this work, we propose a new approach for handling inverse problems with latent diffusion models, where a learned degradation function operates within the latent space, emulating a known image space degradation. Usage of the learned operator reduces the dependency on the Autoencoder to only the initial and final steps of the restoration process, facilitating faster sampling and superior restoration quality. We demonstrate the effectiveness of our method on a variety of image restoration tasks and datasets, achieving significant improvements over prior art.

Time series data are inherently functions of time, yet current transformers often learn time series by modeling them as mere concatenations of time periods, overlooking their functional properties. In this work, we propose a novel objective for transformers that learn time series by re-interpreting them as temporal functions. We build an alternative sequence of time series by constructing degradation operators of different intensity in the functional space, creating augmented variants of the original sample that are abstracted or simplified to different degrees. Based on the new set of generated sequence, we train an autoregressive transformer that progressively recovers the original sample from the most simplified variant. Analogous to the next word prediction task in languages that learns narratives by connecting different words, our autoregressive transformer aims to learn the Narratives of Time Series (NoTS) by connecting different functions in time. Theoretically, we justify the construction of the alternative sequence through its advantages in approximating functions. When learning time series data with transformers, constructing sequences of temporal functions allows for a broader class of approximable functions (e.g., differentiation) compared to sequences of time periods, leading to a 26\% performance improvement in synthetic feature regression experiments. Experimentally, we validate NoTS in 3 different tasks across 22 real-world datasets, where we show that NoTS significantly outperforms other pre-training methods by up to 6\%. Additionally, combining NoTS on top of existing transformer architectures can consistently boost the performance. Our results demonstrate the potential of NoTS as a general-purpose dynamic learner, offering a viable alternative for developing foundation models for time series analysis.

With the development of audio playback devices and fast data transmission, the demand for high sound quality is rising, for both entertainment and communications. In this quest for better sound quality, challenges emerge from distortions and interferences originating at the recording side or caused by an imperfect transmission pipeline. To address this problem, audio restoration methods aim to recover clean sound signals from the corrupted input data. We present here audio restoration algorithms based on diffusion models, with a focus on speech enhancement and music restoration tasks. Traditional approaches, often grounded in handcrafted rules and statistical heuristics, have shaped our understanding of audio signals. In the past decades, there has been a notable shift towards data-driven methods that exploit the modeling capabilities of deep neural networks (DNNs). Deep generative models, and among them diffusion models, have emerged as powerful techniques for learning complex data distributions. However, relying solely on DNN-based learning approaches carries the risk of reducing interpretability, particularly when employing end-to-end models. Nonetheless, data-driven approaches allow more flexibility in comparison to statistical model-based frameworks whose performance depends on distributional and statistical assumptions that can be difficult to guarantee. Here, we aim to show that diffusion models can combine the best of both worlds and offer the opportunity to design audio restoration algorithms with a good degree of interpretability and a remarkable performance in terms of sound quality.

Low-dose computed tomography (CT) images suffer from noise and artifacts due to photon starvation and electronic noise. Recently, some works have attempted to use diffusion models to address the over-smoothness and training instability encountered by previous deep-learning-based denoising models. However, diffusion models suffer from long inference times due to the large number of sampling steps involved. Very recently, cold diffusion model generalizes classical diffusion models and has greater flexibility. Inspired by the cold diffusion, this paper presents a novel COntextual eRror-modulated gEneralized Diffusion model for low-dose CT (LDCT) denoising, termed CoreDiff. First, CoreDiff utilizes LDCT images to displace the random Gaussian noise and employs a novel mean-preserving degradation operator to mimic the physical process of CT degradation, significantly reducing sampling steps thanks to the informative LDCT images as the starting point of the sampling process. Second, to alleviate the error accumulation problem caused by the imperfect restoration operator in the sampling process, we propose a novel ContextuaL Error-modulAted Restoration Network (CLEAR-Net), which can leverage contextual information to constrain the sampling process from structural distortion and modulate time step embedding features for better alignment with the input at the next time step. Third, to rapidly generalize to a new, unseen dose level with as few resources as possible, we devise a one-shot learning framework to make CoreDiff generalize faster and better using only a single LDCT image (un)paired with NDCT. Extensive experimental results on two datasets demonstrate that our CoreDiff outperforms competing methods in denoising and generalization performance, with a clinically acceptable inference time. Source code is made available at https://github.com/qgao21/CoreDiff.

--While Deep Neural Networks (DNNs) trained for image and video super-resolution regularly achieve new state-of-the-art performance, they also suffer from significant drawbacks. One of their limitations is their tendency to generate strong artifacts in their solution. This may occur when the low-resolution image formation model does not match that seen during training. Artifacts also regularly arise when training Generative Adversarial Networks for inverse imaging problems. In this paper, we propose an efficient, fully self-supervised approach to remove the observed artifacts. More specifically, at test time, given an image and its known image formation model, we fine-tune the parameters of the trained network and iteratively update them using a data consistency loss. We apply our method to image and video super-resolution neural networks and show that our proposed framework consistently enhances the solution originally provided by the neural network. In the past decade, the application of Deep Neural Networks (DNNs) to solving inverse imaging problems has gained considerable popularity [ 2 ]. The observed image y is assumed to come from a known image formation model with degradation operator A, which we formulate here as y Ax ǫ, where ǫ denotes the noise. The parameters ψ are learned through a lengthy training stage which requires the use of a large dataset of input-output (y, x) pairs. The training data is commonly generated by applying the degradation operator A to the clean images to obtain the corresponding degraded images used for training. With this straightforward framework combined with the fast-growing nature of Deep Learning, new state-of-the-art results for image restoration tasks are regularly achieved. Preliminary results of this work were presented at the 2019 IEEE International Conference on Image Processing (ICIP) [ 1 ].