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).
In time-series generation, existing approaches typically handcraft ortrain a separate model for each dataset, which hinders their scalability and fails to leverage shared temporal structures across domains. To address this fragmentation, we propose UPLOTS, a Unified, Prompt-guided Language model framework fOr constrained Time-Series Generation across diverse domains. Instead of building task-specific models, UPLOTS leverages a single pre-trained transformer backbone guided by learned constraint prompts, enabling on-demand generation with precise pattern control. One key innovation is our dynamic multi-dataset loss re-weighting and prompt-to-pattern mapping, which allows UPLOTS to internalize diverse temporal structures during training and conditionally generate them at inference. We evaluate UPLOTS on four real-world benchmarks and multiple constraint settings, including peak-period, calendar, load-level, and volatility patterns. Additional held-out constraint-combination and downstream forecasting experiments further demonstrate that UPLOTS generalizes beyond the original peak-pattern setting and improves data augmentation under scarce real-data regimes. Our code and baselines are available at github repo: https://github.com/cruiseresearchgroup/UPLOTS.
Du Yin, Hao Xue, Jinliang Deng +4
University of New South Wales Sydney, NSW, Australia · HKUST(GZ) China · BUAA Beijing, China
Recent advances in generative modeling have substantially improved time series generation, yet most existing methods either assume a regular temporal grid or focus on feature dynamics under a given sampling structure. This makes them illsuited for generating irregular time series in their native form, where a model must capture not only feature values, but also how many observations occur, when they occur, and which features are observed together. To address this heterogeneous generation problem, we propose ChronoFlow, a unified hierarchical flow matching framework organized by statistical granularity. Following a coarse-to-fine hierarchy, ChronoFlow first generates observation counts and feature-wise frequencies, then jointly generates observation times and feature co-observation patterns, and finally generates values conditioned on the realized pattern. This turns a complex joint generation problem into structurally aligned subproblems while preserving their dependencies. To evaluate complete irregular time series generation, we introduce complementary metrics spanning sample realism, sampling structure, value fidelity, and temporal and cross-feature dependencies, and validate them through controlled corruptions. Across five benchmarks, ChronoFlow achieves strong improvements in generation fidelity over existing baselines, while factorization studies support the proposed hierarchy. Our code is available at https://anonymous.4open.science/r/ChronoFlow.
Time-series data are inherently multiscale, spanning diverse temporal granularities from coarse trends to fine-scale dynamics. However, existing time-series generative models provide limited control over the temporal granularity of both inputs and outputs, restricting their ability to condition on user-provided coarse sketches and generate samples at a desired target granularity. To address this, we introduce TimeTok, a unified framework for Granularity-Controllable Time-Series Generation (GC-TSG), which generates time series at any target granularity from any coarser input (e.g., rough sketches) or without conditioning. At the core of TimeTok is a hierarchical tokenization strategy that maps time series into an ordered sequence of tokens, from coarse to fine temporal granularity. Our autoregressive generation process operates across these granularity levels, producing token blocks that are decoded back into continuous time series. This design naturally enables GC-TSG within a single framework, where controlling the number of token blocks provides explicit control over output detail. Experiments show that TimeTok excels at GC-TSG tasks while achieving state-of-the-art performance in standard generation. Furthermore, we showcase TimeTok's potential as a foundational tokenizer by training on multiple datasets with heterogeneous temporal granularities, verifying strong transferability that consistently outperforms models trained on individual datasets. To our knowledge, this is the first unified framework that covers the full generative spectrum for time series, offering a valuable foundation for models that benefit from diverse temporal granularities.
Seokhyun Lee, Jaeho Kim, Changjun Oh +2
Department of Artificial Intelligence, Korea University, Seoul, South Korea · Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom.