Diffusion models have shown great promise in data generation, yet generating time series data remains challenging due to the need to capture complex temporal dependencies and structural patterns. In this paper, we present \textit{TSGDiff}, a novel framework that rethinks time series generation from a graph-based perspective. Specifically, we represent time series as dynamic graphs, where edges are constructed based on Fourier spectrum characteristics and temporal dependencies. A graph neural network-based encoder-decoder architecture is employed to construct a latent space, enabling the diffusion process to model the structural representation distribution of time series effectively. Furthermore, we propose the Topological Structure Fidelity (Topo-FID) score, a graph-aware metric for assessing the structural similarity of time series graph representations. Topo-FID integrates two sub-metrics: Graph Edit Similarity, which quantifies differences in adjacency matrices, and Structural Entropy Similarity, which evaluates the entropy of node degree distributions. This comprehensive metric provides a more accurate assessment of structural fidelity in generated time series. Experiments on real-world datasets demonstrate that \textit{TSGDiff} generates high-quality synthetic time series data generation, faithfully preserving temporal dependencies and structural integrity, thereby advancing the field of synthetic time series generation.