Time-Dependent Graph Generation: A Survey of Discrete-Time and Continuous-Time Perspectives

Recent advances in graph generative modeling have increasingly reframed graph generation as the problem of learning probability paths that transport simple reference distributions toward complex graph distributions. This time-dependent perspective unifies a broad spectrum of generative paradigms, including finite-step denoising, masking, editing, and refinement methods, as well as continuous-time flows, score-based and diffusion models, Schrödinger bridge formulations, and continuous-time Markov processes over discrete graph states. In this survey, we present a unified temporal and transport-based framework for graph generation, organizing existing methods according to their time parameterization, state space, probability-path construction, evolution dynamics, training objectives, and sampling mechanisms. By systematically comparing discrete-time and continuous-time formulations, we reveal fundamental connections between seemingly disparate model families and highlight the design trade-offs governing scalability, structural fidelity, controllability, interpretability, and computational efficiency. We further review evaluation protocols, benchmark datasets, and key application domains, and identify emerging challenges in permutation symmetry, graph validity, large-scale generation, reproducibility, and fair empirical comparison.