  Graph generation has emerged as a crucial task in machine learning, with
significant challenges in generating graphs that accurately reflect specific
properties. Existing methods often fall short in efficiently addressing this
need as they struggle with the high-dimensional complexity and varied nature of
graph properties. In this paper, we introduce the Neural Graph Generator (NGG),
a novel approach which utilizes conditioned latent diffusion models for graph
generation. NGG demonstrates a remarkable capacity to model complex graph
patterns, offering control over the graph generation process. NGG employs a
variational graph autoencoder for graph compression and a diffusion process in
the latent vector space, guided by vectors summarizing graph statistics. We
demonstrate NGG's versatility across various graph generation tasks, showing
its capability to capture desired graph properties and generalize to unseen
graphs. This work signifies a significant shift in graph generation
methodologies, offering a more practical and efficient solution for generating
diverse types of graphs with specific characteristics.
