Graph2TS: Structure-Controlled Time Series Generation via Quantile-Graph VAEs
Authors: Shaoshuai Du, Joze M. Rozanec, Andy Pimentel, Ana-Lucia Varbanescu
Organizations: Informatics Institute, University of Amsterdam, Amsterdam, The Netherlands · Computer Architecture for Embedded Systems, University of Twente, Enschede, The Netherlands · Laboratory of Artificial Intelligence, Institute Jozef Stedan, Ljubljana, Slovenia
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.
Figures & tables
Figure 1: Example of time-series to Quantile Graph mapping. Left: The time series is discretized into states based on quantile boundaries. Right: The resulting Markov transition dynamics represented as a graph.
Figure 2: The Architecture of Our Proposed Graph2TS
Table 2: Ablation study on ECG dataset. We compare the full model with (i) identity graph conditioning (w/o graph) and (ii) a deterministic Graph2TS model without stochastic latent variables. Lower is better ( ↓ ), higher is better ( ↑ ).
Figure 3: Ablation study visualizing the impact of structural conditioning and stochastic residual modeling. Rows (top to bottom): Autocorrelation Function (ACF), Power Spectral Density (PSD), and t-SNE visualization. Columns (left to right): The proposed Full Model, the model without the graph module (w/o Graph), and the model without the stochastic component (w/o Stochasticity). Removing stochasticity leads to pronounced spectral energy collapse and mode contraction, while removing the graph weakens and destroy low-frequency temporal structure.
Table 3: Ablation study on CHB-MIT and Sunspot datasets. Each row removes or modifies a single loss component. Metrics: Wass : Wasserstein distance, KS : KS statistic, ACF : ACF MAE, PSD : PSD L2 distance, P-Err : ProtoErr, Cov : Coverage@ τ0.5 . ( ↓ : Lower is better, ↑ : Higher is better).
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
B
x statistics
Δx statistics
mean
std
excess kurt.
quantile range (0.1% → 99.9%)
mean
std
excess kurt.
Sunspot
1758
-0.0360
0.9668
0.5321
[-1.0741, 3.5320]
-7.5e-05
0.1994
2.2466
ECG
20312
0.2148
0.8283
7.3562
[-1.6078, 5.1106]
4.4e-05
0.1819
41.5587
Appendix
Table 4: Distribution statistics in z-score space for Sunspot vs ECG windows (length T=32 ). We report summary statistics for raw values x and first-order differences Δx . Excess kurtosis indicates tail-heaviness (larger ⇒ heavier tails).
Figure 4: Sunspot vs ECG in z-score space . ECG exhibits substantially heavier tails, especially in Δx , indicating more frequent abrupt transitions compared to the smoother Sunspot dynamics.
Figure 5: Visualization of real time series and corresponding generated time series. Each row (a, b, c) displays 10 samples generated from a single, distinct graph topology, illustrating the model’s ability to synthesize data corresponding to different graphs.
Figure 6: Qualitative comparison between real and generated data across three distinct samples. Each row visualizes the Real Time Series and Real Quantile Graph (left panels) alongside the Generated Time Series and Generated Quantile Graph (right panels), demonstrating the model’s capability to capture both temporal dynamics and structural dependencies.
Figure 7: Mean autocorrelation functions (ACF) of generated time series on four datasets. Rows (top to bottom): CHB-MIT, Sunspot, Electricity, and ECG. Columns: Models. The proposed Graph2TS consistently preserves temporal dependency patterns of the real data across all datasets, while DiffusionTS exhibits over-smoothing and TimeGAN shows increased structural deviation.
Figure 8: Mean power spectral density (PSD) of generated time series on four datasets. Rows (top to bottom): CHB-MIT, Sunspot, Electricity, and ECG. The proposed model Graph2TS closely matches the spectral profile of real data across all datasets, whereas DiffusionTS tends to attenuate high-frequency components and TimeGAN exhibits spectral distortion.
Figure 9: t-SNE visualization of generated time series on four datasets. Rows (top to bottom): CHB-MIT, Sunspot, Electricity, and ECG. Red points represent real data and blue points represent generated data. Our Graph2TS model demonstrates superior overlap with the real data distribution, indicating it captures the global structural properties more effectively than baselines.
Figure 10: Deterministic graph to time series model (Graph2TS without stochasticity).
Department of Artificial Intelligence, Korea University, Seoul, South Korea · Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom.