Related papers: Diffusion determines the recurrent graph

We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. Under minimal structural assumptions on the graph, we…

We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

We consider the identification of nonlinear diffusion coefficients of the form $a(t,u)$ or $a(u)$ in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assumptions using…

We consider a hierarchy of graph invariants that naturally extends the spectral invariants defined by F\"urer (Lin. Alg. Appl. 2010) based on the angles formed by the set of standard basis vectors and their projections onto eigenspaces of…

Diffusion models achieve state-of-the-art performance in generating realistic objects and have been successfully applied to images, text, and videos. Recent work has shown that diffusion can also be defined on graphs, including graph…

We prove under a weak smoothness condition that two Riemannian manifold are isomorphic if and only there exists an order isomorphism which intertwines with the Dirichlet type heat semigroups on the manifolds.

Autoregressive models excel in efficiency and plug directly into the transformer ecosystem, delivering robust generalization, predictable scalability, and seamless workflows such as fine-tuning and parallelized training. However, they…

Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly one-shot generative models that apply Gaussian diffusion in the…

Graph diffusion models have emerged as state-of-the-art techniques in graph generation; yet, integrating domain knowledge into these models remains challenging. Domain knowledge is particularly important in real-world scenarios, where…

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…

We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…

Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive…

Continuous graph neural models based on differential equations have expanded the architecture of graph neural networks (GNNs). Due to the connection between graph diffusion and message passing, diffusion-based models have been widely…

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…

We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the…

We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms are based on contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is…

Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are…