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State-of-the-art atmospheric turbulence image restoration methods utilize standard image processing tools such as optical flow, lucky region and blind deconvolution to restore the images. While promising results have been reported over the…

The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…

We prove a comparison theorem for the isoperimetric profiles of simple closed curves evolving by the normalized curve shortening flow: If the isoperimetric profile of the region enclosed by the initial curve is greater than that of some…

Diffusion models have recently been recognised as efficient inverse problem solvers due to their ability to produce high-quality reconstruction results without relying on pairwise data training. Existing diffusion-based solvers utilize…

Diffusion models have emerged as the leading approach for image synthesis, demonstrating exceptional photorealism and diversity. However, training diffusion models at high resolutions remains computationally prohibitive, and existing…

We consider a class of inverse problems characterized by forward operators that are partially specified, non-smooth, and non-differentiable. Although generative inverse solvers have made significant progress, we find that these forward…

Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

Accurate blur estimation is essential for high-performance imaging across various applications. Blur is typically represented by the point spread function (PSF). In this paper, we propose a physics-informed PSF learning framework for…

Robotic manipulation in unstructured environments requires the generation of robust and long-horizon trajectory-level policy with conditions of perceptual observations and benefits from the advantages of SE(3)-equivariant diffusion models…

Existing deep learning based visual servoing approaches regress the relative camera pose between a pair of images. Therefore, they require a huge amount of training data and sometimes fine-tuning for adaptation to a novel scene.…

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch,…

Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…

Time series of observables measured from complex systems do often exhibit non-normal statistics, their statistical distributions (PDF's) are not gaussian and often skewed, with roughly exponential tails. Departure from gaussianity is…

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…

High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence,…

The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…

A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…