Geometric and Diffusion-Based Methods in Graph Generation and Signal Processing

The field of graph generation and signal processing is witnessing a significant shift towards geometric and diffusion-based methods. Researchers are increasingly focusing on capturing the underlying structure and geometry of graphs, rather than just their spectral properties. This is evident in the development of novel frameworks that integrate spectral geometry with flow matching, allowing for more efficient and scalable generation of diverse graphs. Additionally, diffusion-based models are being explored for graph signal generation, enabling the creation of synthetic data that preserves essential temporal and spectral properties of real data. Noteworthy papers in this area include Graph Generation with Spectral Geodesic Flow Matching, which proposes a novel framework for graph generation using spectral eigenmaps and geodesic flows. Another notable work is Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction, which introduces a Riemannian diffusion model for capturing distinct manifold signatures of complex graph data. RareGraph-Synth is also worth mentioning, as it presents a knowledge-guided diffusion framework for generating realistic yet privacy-preserving synthetic patient trajectories in ultra-rare diseases.

Sources

Graph Generation with Spectral Geodesic Flow Matching

Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction

Forecasting-Based Biomedical Time-series Data Synthesis for Open Data and Robust AI

Graph-Aware Diffusion for Signal Generation

Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures

RareGraph-Synth: Knowledge-Guided Diffusion Models for Generating Privacy-Preserving Synthetic Patient Trajectories in Ultra-Rare Diseases

Graph Conditioned Diffusion for Controllable Histopathology Image Generation

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