Related papers: Calibrated Semantic Diffusion: A p-Laplacian Synth…

The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…

Denoising models such as Diffusion or Flow Matching have recently advanced generative modeling for discrete structures, yet most approaches either operate directly in the discrete state space, causing abrupt state changes. We introduce…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed…

Over recent years, denoising diffusion generative models have come to be considered as state-of-the-art methods for synthetic data generation, especially in the case of generating images. These approaches have also proved successful in…

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…

In this paper we study numerical approximations of the evolution problem for the nonlocal $p$-Laplacian with homogeneous Neumann boundary conditions. First, we derive a bound on the distance between two continuous-in-time trajectories…

This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…

This paper focuses on the consensus averaging problem on graphs under general noisy channels. We study a particular class of distributed consensus algorithms based on damped updates, and using the ordinary differential equation method, we…

Iterative refinement methods based on a denoising-inversion cycle are powerful tools for enhancing the quality and control of diffusion models. However, their effectiveness is critically limited when combined with standard Classifier-Free…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

This paper studies a class of $p$-Laplacian equations on point clouds that arise from hypergraph learning in a semi-supervised setting. Under the assumption that the point clouds consist of independent random samples drawn from a bounded…

Graph-based Retrieval-Augmented Generation (RAG) systems leverage interconnected knowledge structures to capture complex relationships that flat retrieval struggles with, enabling multi-hop reasoning. Yet most existing graph-based methods…

Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…

Global Navigation Satellite Systems (GNSS) are vital for reliable urban positioning. However, multipath and non-line-of-sight reception often introduce large measurement errors that degrade accuracy. Learning-based methods for predicting…

This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…

We introduce a framework for joint grounded scene graph - image generation, a challenging task involving high-dimensional, multi-modal structured data. To effectively model this complex joint distribution, we adopt a factorized approach:…

We develop a convex framework for spatially varying coefficient quantile regression that, for each predictor, separates a location-invariant \emph{global} effect from a \emph{spatial deviation}. An adaptive group penalty selects whether a…

Recent advances in Graph Neural Networks (GNNs) have revolutionized graph-structured data modeling, yet traditional GNNs struggle with complex heterogeneous structures prevalent in real-world scenarios. Despite progress in handling…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…