Although recent generative models can produce time series with close marginal distributions, they often face a fundamental tension between preserving global temporal structure and modeling stochastic local variations, particularly for highly volatile signals with weak or irregular periodicity. Direct distribution matching in such settings can amplify noise or suppress meaningful temporal patterns. In this work, we propose a structure-residual perspective on time-series generation, viewing temporal data as the combination of a structural backbone and stochastic residual dynamics, thereby motivating the separation of global organization from sample-level variability. Based on this insight, we represent time-series structure using a quantile-based transition graph that compactly captures global distributional and temporal dependencies. Building on this representation, we propose Graph2TS, a quantile-graph conditioned variational autoencoder that performs cross-modal generation from structural graphs to time series. By conditioning generation on structure rather than labels or metadata, the model preserves global temporal organization while enabling controlled stochastic variation. Experiments on diverse datasets, including sunspot, electricity load, ECG, and EEG signals, demonstrate improved distributional fidelity, temporal alignment, and representativeness compared to diffusion- and GAN-based baselines, highlighting structure-controlled and cross-modal generation as a promising direction for time-series modeling.

翻译：尽管当前生成模型能够生成边缘分布相近的时间序列，但在保留全局时间结构与建模随机局部变化之间往往存在根本性矛盾，尤其是对于弱周期或不规则周期的高波动信号。在此类场景下，直接进行分布匹配可能放大噪声或抑制有意义的时间模式。本文提出一种基于结构-残差视角的时间序列生成方法，将时序数据视为结构主干与随机残差动态的组合，从而推动将全局组织与样本级变异性分离。基于此观点，我们利用基于分位数的转移图表示时间序列结构，该图紧凑地捕获了全局分布和时序依赖关系。在此表示基础上，我们提出Graph2TS——一种基于分位数图条件变分自编码器，实现从结构图到时间序列的跨模态生成。通过以结构而非标签或元数据作为生成条件，模型在保留全局时间组织的同时实现可控随机变化。在包括太阳黑子、电力负荷、心电图和脑电图信号等多个数据集上的实验表明，与基于扩散和生成对抗网络的基线方法相比，本方法在分布保真度、时间对齐性和代表性方面均有所提升，凸显了结构可控的跨模态生成作为时间序列建模的一个有前景方向。