arXiv Machine Learning

Network Denoising Revisited: A Ricci-Flow-Inspired Graph Diffusion Method

The paper introduces Ricci-Diffusion, a graph denoising technique that uses curvature-guided diffusion inspired by Ricci flow. Unlike traditional similarity-driven methods, it modulates local transport in the diffusion kernel based on edge-level curvature, steering edge-weight updates toward a more regular graph geometry. The authors provide theoretical analysis showing curvature’s ability to distinguish graph structures and induce first-order corrections, and demonstrate that the method converges to a stable denoised network, improving structure recovery and downstream performance on real-world and synthetic graphs.

arXiv Machine Learning

Jul 27

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature

arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.

By Rachid Caich, Yassine Abbahaddou

efficiency benchmarks

arXiv AI

Aug 26

Ollivier-Ricci Curvature of Riemannian Manifolds and Directed Graphs with Applications to Graph Neural Networks

arXiv:2604.14211v2 Announce Type: replace-cross Abstract: This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserste...

By Eleanor P Wiesler

arXiv AI

Sep 15

Geometric Flow enhanced Graph Coarsening

The paper introduces RicciPool, a graph pooling method that incorporates higher‑order connectivity via Ollivier‑Ricci curvature to reweight edges before spectral clustering. Unlike traditional pooling approaches that focus only on rough topology, RicciPool leverages local connection information to improve cluster assignment. Experiments on protein and social network datasets demonstrate its effectiveness.

By Chaoqun Fei, Guoxuan Li, Tinglve Zhou, Chuanqing Wang, Yangyang Li

arXiv Machine Learning

4d ago

A Finslerian Approach for Embedding Directed Data

arXiv:2609.37649v1 Announce Type: cross Abstract: Many datasets carry an intrinsic directionality: citations point backward in time, cells differentiate along lineages, and traffic follows preferred...

By Gwendal Debaussart-Joniec (CB, ENS Paris Saclay), Th\'eau Blanchard (HeKA | U1346, GE Healthcare), Argyris Kalogeratos (CB, ENS Paris Saclay)

rag diffusion

arXiv Machine Learning

Jun 29

Directed Graph Topology Inference via Graph Filter Identification

arXiv:2606. 27455v1 Announce Type: cross Abstract: We address the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics on the sought graph.

By Rasoul Shafipour, Andrei Buciulea, Santiago Segarra, Antonio G. Marques, Gonzalo Mateos

diffusion

arXiv AI

Jul 9

Diffusion enabled Optimal Transport distances for graph matching

arXiv:2607. 06646v1 Announce Type: cross Abstract: This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport.

By Iman Seyedi, Francesco Archetti

diffusion

arXiv Machine Learning

Jun 18

Enhanced Graph Neural Networks using K-Hop Gaussian Diffusion

arXiv:2606. 18317v1 Announce Type: new Abstract: Most graph neural network (GNN) cores rely on graph convolutions, typically implemented as message passing between direct (single-hop) neighbors.

By Xuling Zhang, Peng Wang, Daiyan Li, Aoran Huang, Zeiwei Chen, Yongkui Yang

diffusion benchmarks

arXiv Machine Learning

Sep 1

Accelerate Vector Diffusion Maps by Landmarks

The paper introduces LA-VDM, a landmark‑constrained algorithm that speeds up Vector Diffusion Maps (VDM) by employing a two‑stage normalization to handle nonuniform sampling in both data and landmark sets. It demonstrates that, under a manifold model with a frame bundle structure, LA‑VDM can accurately recover parallel transport from a point cloud and asymptotically converges to the connection Laplacian. Experiments on simulated data and a nonlocal image denoising application confirm the method’s performance and accuracy.

By Sing-Yuan Yeh, Yi-An Wu, Hau-Tieng Wu, Mao-Pei Tsui

diffusion

Hugging Face Trending Papers

Jun 16

Enhanced Graph Neural Networks using K-Hop Gaussian Diffusion

Most graph neural network (GNN) cores rely on graph convolutions, typically implemented as message passing between direct (single-hop) neighbors. In many real-world graphs, edges can be noisy or poorly defined, limiting information propagation to local neighborhoods.

diffusion benchmarks

arXiv AI

Aug 10

Fluid-DiT: Graph-Free Diffusion Transformers for Fluid Flow Simulations Learning

arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.

By Shentong Mo, Guolin Ke

llms diffusion benchmarks

arXiv AI

Jun 11

From Uniform to Learned Graph Priors: Diffusion for Structure Discovery

arXiv:2606. 11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges.

By Qi Shao, Hao Guo, Jiawen Chen, Duxin Chen, Wenwu Yu

diffusion benchmarks

Hugging Face Trending Papers

Jul 8

DiPhon: Diffusion on Graphons for Scalable Graph Generation

Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem.

diffusion

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