Generating realistic graphs faces challenges in estimating accurate distribution of graphs in an embedding space while preserving structural characteristics. However, existing graph generation methods primarily focus on approximating the joint distribution of nodes and edges, often overlooking topological properties such as connected components and loops, hindering accurate representation of global structures. To address this issue, we propose a Topology-Aware diffusion-based Graph Generation (TAGG), which aims to sample synthetic graphs that closely resemble the structural characteristics of the original graph based on persistent homology. Specifically, we suggest two core components: 1) Persistence Diagram Matching (PDM) loss which ensures high topological fidelity of generated graphs, and 2) topology-aware attention module (TAM) which induces the denoising network to capture the homological characteristics of the original graphs. Extensive experiments on conventional graph benchmarks demonstrate the effectiveness of our approach demonstrating high generation performance across various metrics, while achieving closer alignment with the distribution of topological features observed in the original graphs. Furthermore, application to real brain network data showcases its potential for complex and real graph applications.

A Marked Temporal Point Process (MTPP) is a stochastic process whose realization is a set of event-time data. MTPP is often used to understand complex dynamics of asynchronous temporal events such as money transaction, social media, healthcare, etc. Recent studies have utilized deep neural networks to capture complex temporal dependencies of events and generate embedding that aptly represent the observed events. While most previous studies focus on the inter-event dependencies and their representations, how individual events influence the overall dynamics over time has been under-explored. In this regime, we propose a Decoupled MTPP framework that disentangles characterization of a stochastic process into a set of evolving influences from different events. Our approach employs Neural Ordinary Differential Equations (Neural ODEs) to learn flexible continuous dynamics of these influences while simultaneously addressing multiple inference problems, such as density estimation and survival rate computation. We emphasize the significance of disentangling the influences by comparing our framework with state-of-the-art methods on real-life datasets, and provide analysis on the model behavior for potential applications.