Related papers: Diffusion Models for Cayley Graphs

Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but…

Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…

Existing approaches for diffusion on graphs, e.g., for label propagation, are mainly focused on isotropic diffusion, which is induced by the commonly-used graph Laplacian regularizer. Inspired by the success of diffusivity tensors for…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interaction kernels of the aggregation system, which characterize the…

In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…

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…

In the present paper, we study Neumaier Cayley graphs. First, we give a criterion for a Cayley graph to be a Neumaier graph with a spread given by the cosets of a subgroup. Further, we construct a new infinite family of Neumaier Cayley…

Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight…

In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite $k$-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by…

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 study a hybrid computational model for integer factorization in which the only non-classical resource is access to an \emph{iterated diffusion process} on a finite graph. Concretely, a \emph{diffusion step} is defined to be one…

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…

In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…

Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…

Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as…

Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…

We study the behavior of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities) and also large macro-scale clusters by varying a…

There has been a flurry of activity around using pretrained diffusion models as informed data priors for solving inverse problems, and more generally around steering these models using reward models. Training-free methods like diffusion…