Related papers: Solving Linear Inverse Problems using Higher-Order…

We investigate the theoretical properties of general diffusion (interpolation) paths and their Langevin Monte Carlo implementation, referred to as diffusion annealed Langevin Monte Carlo (DALMC), under weak conditions on the data…

Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

Diffusion models have become the de facto standard for modern visual generation, including well-established frameworks such as latent diffusion and flow matching. Recently, modeling high-order dynamics has emerged as a promising frontier in…

Diffusion models have shown remarkable progress in various generative tasks such as image and video generation. This paper studies the problem of leveraging pretrained diffusion models for performing discriminative tasks. Specifically, we…

In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using…

We introduce a novel class of score-based diffusion processes that operate directly in the representation space of Lie groups. Leveraging the framework of Generalized Score Matching, we derive a class of Langevin dynamics that decomposes as…

In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…

Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance…

Imaging inverse problems can be solved in an unsupervised manner using pre-trained diffusion models, but doing so requires approximating the gradient of the measurement-conditional score function in the diffusion reverse process. We show…

Inverse rendering, the process of inferring scene properties from images, is a challenging inverse problem. The task is ill-posed, as many different scene configurations can give rise to the same image. Most existing solutions incorporate…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…

We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive…

This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…

Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…

The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…