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Diffusion-weighted magnetic resonance imaging (dMRI) is the only non-invasive tool for studying white matter tracts and structural connectivity of the brain. These assessments rely heavily on tractography techniques, which reconstruct…

Diffusion-weighted imaging (DWI) is a type of Magnetic Resonance Imaging (MRI) technique sensitised to the diffusivity of water molecules, offering the capability to inspect tissue microstructures and is the only in-vivo method to…

The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Penalized empirical risk minimization with a surrogate loss function is often used to learn a high-dimensional linear decision rule in classification problems. Although much of the literature focus on the generalization error, there is a…

The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging and longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance…

How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usually used to train diffusion models is the score function of…

In the paper, a new method of blind estimation of noise variance in a single highly textured image is proposed. An input image is divided into 8x8 blocks and discrete cosine transform (DCT) is performed for each block. A part of 64 DCT…

We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard…

Removing or repairing the imperfections of a digital images or videos is a very active and attractive field of research belonging to the image inpainting technique. This later has a wide range of applications, such as removing scratches in…

Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then…

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…

We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model…

We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we…

Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a…

Seismic noise cross correlations are used to image crustal structure and heterogeneity. Typically, seismic networks are only anisotropically illuminated by seismic noise, a consequence of the non-uniform distribution of sources. Here, we…

Real-world image super-resolution (RWSR) is a long-standing problem as low-quality (LQ) images often have complex and unidentified degradations. Existing methods such as Generative Adversarial Networks (GANs) or continuous diffusion models…

Understanding diffusion in microstructures plays a crucial role in many scientific fields, including neuroscience, cancer or energy research. While magnetic resonance (MR) methods are the gold standard for diffusion measurements, spatial…

Despite the remarkable success, recent reconstruction-based anomaly detection (AD) methods via diffusion modeling still involve fine-grained noise-strength tuning and computationally expensive multi-step denoising, leading to a fundamental…