Title: Score-Based Graph Generative Modeling with Self-Guided Latent Diffusion. Abstract: Graph generation is a fundamental task in machine learning, and it is critical for numerous real-world applications, biomedical discovery and social science. Existing diffusion-based graph generation methods have two limitations: (i) they conduct diffusion process directly in complex graph space (i.e., node feature, adjacency matrix, or both), resulting in hard optimization with network evaluations; (ii) they usually neglect to sufficiently cover the whole distribution of target unlabeled graph set and thus fail to make semantic controllable generation. In this paper, we first propose a unified latent-based graph generative framework, Score-Based Graph Generative Model (SGGM), powered by Self-Guided Latent Diffusion (SLD) to address both limitations. Specifically, we pretrain a variational graph autoencoder to map raw graph of high-dimensional discrete space to low-dimensional topology-injected latent space, and apply score-based generative model there, yielding a smoother, faster and more expressive graph generation procedure. To sufficiently cover the whole semantical distribution of unlabeled graph set, we propose SLD to make controllable self-guidance of the sample generation with gradients from the designed assigning function towards the hierarchical pseudo label, produced by iteratively clustering on the latent embeddings. In addition, we conduct periodic update on the pseudo label in training process to achieve mutual adaptation between self-guidance and score-based generation. Experiments show that our SGGM powered by SLD outperforms previous graph generation baselines on both generic and molecular graph datasets, demonstrating the generality and extensibility along with further theoretical proofs.