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

arXiv: https://arxiv.org/abs/2608.16923 · HTML: https://mlsanity.com/paper/2608.16923/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature](https://mlsanity.com/paper/2211.15779/) (2022)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Self-Supervised Graph Structure Refinement for Graph Neural Networks](https://mlsanity.com/paper/2211.06545/) (2022)
- [Network Enhancement: a general method to denoise weighted biological networks](https://mlsanity.com/paper/1805.03327/) (2018)
- [A Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness](https://mlsanity.com/paper/1908.01596/) (2019)

## Abstract (arXiv)

Networks provide a fundamental representation of relationships among entities. However, real-world networks are often corrupted by noise caused by measurement errors and inherent stochasticity, hindering the discovery of meaningful structure. Most denoising methods rely on similarity-driven diffusion and ignore the non-Euclidean geometry of graphs, where local variations induce heterogeneous information transport. This motivates a geometric revisit of network denoising. In this work, we propose Ricci-Diffusion, a curvature-guided graph diffusion method inspired by Ricci flow. Specifically, Ricci-Diffusion exhibits a Ricci-flow-like evolution, in which relative edge-level curvature modulates local transport in the diffusion kernel and guides edge-weight updates toward a more regular graph geometry. We further provide a theoretical analysis showing that curvature can distinguish graph structures that common similarity-driven diffusion kernels fail to separate, and that curvature induces first-order corrections in one-step diffusion updates. The resulting diffusion process explicitly characterizes transport heterogeneity across local geometries and admits theoretical convergence to a stable denoised network. Results on real-world and synthetic graphs show that curvature-guided updates and curvature homogenization improve structure recovery and downstream performance.