<ul data-eligibleForWebStory="true">The simulation of discrete karst networks is challenging due to complex physicochemical processes in geological and hydrogeological contexts.A novel approach using graph generative models to represent karst networks has been proposed.Karst networks are represented as graphs with nodes containing spatial information and edges indicating connections between nodes.The generative process involves utilizing graph recurrent neural networks (GraphRNN) to learn the topological distribution of karst networks.Denoising diffusion probabilistic models on graphs (G-DDPM) are used to learn node features like spatial coordinates.The approach aims to generate realistic karst networks that capture essential features of the original data.Real-world karst networks were used to test the approach by comparing generated subgraphs with actual subgraphs.Geometry and topology metrics were employed to evaluate the generated subgraphs.The methodology allows for stochastic simulation of discrete karst networks across various formations.It serves as a useful tool for studying physical processes such as flow and transport in karst environments.