Related papers: Measurement-Consistent Langevin Corrector for Stab…

Latent diffusion models offer an attractive alternative to discrete diffusion for non-autoregressive text generation by operating on continuous text representations and denoising entire sequences in parallel. The major challenge in latent…

Limited-angle computed tomography (LACT) reconstruction is an inverse problem with severe ill-posedness arising from missing projection angles, and it is difficult to restore high-precision images without sufficient prior knowledge. In…

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…

Recent video generative models have demonstrated impressive visual fidelity, yet they often struggle with semantic, geometric, and identity consistency. In this paper, we propose a system-level framework, termed the Divide-and-Conquer…

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce…

We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous Galerkin spectral element methods (DGSEM). The use of Legendre-Gauss-Lobatto (LGL) quadrature endows collocated DGSEM space discretizations of nonlinear…

We provide a method to design adaptive controllers for nonlinear systems using model predictive control (MPC). By combining a certainty-equivalent MPC formulation with least-mean-square parameter adaptation, we obtain an adaptive controller…

This project develops a self correcting framework for large language models (LLMs) that detects and mitigates hallucinations during multi-step reasoning. Rather than relying solely on final answer correctness, our approach leverages fine…

Modern successes of diffusion models in learning complex, high-dimensional data distributions are attributed, in part, to their capability to construct diffusion processes with analytic transition kernels and score functions. The…

Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…

There is a growing interest in the use of latent diffusion models (LDMs) for image restoration (IR) tasks due to their ability to model effectively the distribution of natural images. While significant progress has been made, there are…

Sparse-view computed tomography (CT) reconstruction is fundamentally challenging due to undersampling, leading to an ill-posed inverse problem. Traditional iterative methods incorporate handcrafted or learned priors to regularize the…

This paper presents an uncertainty compensation-based robust adaptive model predictive control (MPC) framework for linear systems with both matched and unmatched nonlinear uncertainties subject to both state and input constraints. In…

We propose model predictive funnel control, a novel model predictive control (MPC) scheme building upon recent results in funnel control. The latter is a high-gain feedback methodology that achieves evolution of the measured output within…

The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…

A conditional latent-diffusion based framework for solving the electromagnetic inverse scattering problem associated with microwave imaging is introduced. This generative machine-learning model explicitly mirrors the non-uniqueness of the…

While Diffusion Language Models (DLMs) are theoretically well-suited for iterative refinement due to their non-causal structure, they often fail to reliably revise incorrect tokens in practice. The key challenge lies in the model's…

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and…

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by…