Graph2TS: Structure-Conditioned Time Series Generation from Quantile Graphs

Time-series generation requires capturing recurring temporal structure while preserving stochastic variation across its realizations. We approach this problem from a structure–residual perspective, representing a time series through a structural condition while modeling the remaining variation stochastically. Based on this perspective, we introduce $\text{Graph2TS}$, a structure-conditioned time-series generator that uses quantile graphs as structural representations. A quantile graph compactly summarizes empirical one-step transitions between globally shared amplitude-quantile states, providing a fixed-size, lossy representation of distributional and local transition structure. Graph2TS conditions generation on this representation and uses a latent variable to model variation not specified by the graph. All graphs and normalization statistics are derived from training data, and generation requires no test-specific conditioning information. Experiments against GAN, diffusion, and flow-matching baselines on four real-world datasets show particularly strong performance on ECG and EEG signals, while remaining competitive on Sunspot and Electricity with dataset-dependent trade-offs. Dataset analysis further suggests that these benefits are most pronounced for volatile signals with weak or irregular periodicity. Additional Electricity experiments up to length 256 show stronger relative performance over DiffusionTS at longer sequence lengths, although coverage decreases as sequence length increases. These results support the structure–residual perspective and suggest graph-based structural representations as a promising direction for time-series generation.