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Diffusion-based generative models are machine learning models that use diffusion processes to learn the probability distribution of high-dimensional data. In recent years, they have become extremely successful in generating multimedia…
Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…
Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…
We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms for Bayesian linear inverse problems. The benchmark synthesizes signals from sparse L\'evy-process priors whose posteriors admit efficient Gibbs methods.…
Diffusion models are now commonly used to solve inverse problems in computational imaging. However, most diffusion-based inverse solvers require complete knowledge of the forward operator to be used. In this work, we introduce a novel…
Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this…
Diffusion models have recently emerged as powerful generative models in medical imaging. However, it remains a major challenge to combine these data-driven models with domain knowledge to guide brain imaging problems. In neuroimaging,…
Diffusion models are widely used as priors in imaging inverse problems. However, their performance often degrades under distribution shifts between the training and test-time images. Existing methods for identifying and quantifying…
Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…
We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of…
The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…
Bayesian Last Layer (BLL) models focus solely on uncertainty in the output layer of neural networks, demonstrating comparable performance to more complex Bayesian models. However, the use of Gaussian priors for last layer weights in…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…