New Ricci-Diffusion method denoises networks by leveraging geometric curvature

Networks underpin everything from social graphs to biological interactions, but real-world data is often noisy due to measurement errors and stochastic processes. Traditional denoising relies on similarity-driven diffusion, which assumes uniform information flow across the graph. That assumption breaks in non-Euclidean geometries where local structure varies. In a new arXiv paper, researchers Ye Fang and Chuan-Xian Ren introduce Ricci-Diffusion, a curvature-guided diffusion method that explicitly accounts for heterogeneous transport by borrowing principles from Ricci flow — a geometric process that smooths curvature over a manifold.

Ricci-Diffusion modulates the diffusion kernel using relative edge-level curvature, steering edge weights toward a more regular geometry. The authors provide theoretical results showing curvature can separate graph structures that common similarity-driven kernels cannot, and that it introduces first-order corrections in one-step diffusion updates. The method guarantees convergence to a stable denoised network. Experiments on both synthetic and real-world graphs demonstrate that curvature-guided updates and homogenization improve structure recovery and downstream task performance. The paper runs 9 pages with 5 figures, and offers a fresh geometric perspective on a classic problem — suggesting that curvature, not just similarity, is the key to robust network denoising.