TSGDiff: Rethinking Synthetic Time Series Generation from a Pure Graph Perspective

Conference: AAAI 2026 arXiv: 2511.12174 Code: TSGDiff Area: image_generation (actually time series generation) Keywords: time series generation, graph neural networks, diffusion models, Fourier transform, topological fidelity

TL;DR

This paper proposes TSGDiff, the first framework to rethink time series generation from a purely graph-based perspective. Time series are represented as dynamic graphs constructed from Fourier spectral features, diffusion modeling is performed in the graph latent space, and a novel Topo-FID metric is introduced to evaluate the structural fidelity of generated time series.

Background & Motivation

1. Background: Multivariate time series generation is in broad demand across energy management, financial forecasting, and medical monitoring. Existing approaches include GAN-based methods (TimeGAN), VAE-based methods (TimeVAE), and diffusion-based methods (Diffusion-TS, CSDI).
2. Limitations of Prior Work: (a) Traditional generative models struggle to effectively capture complex spatio-temporal dependencies among variables; (b) they operate under Euclidean space assumptions and cannot represent the inherent topological and structural features of time series data; (c) methods such as Diffusion-TS employ an encoder-decoder transformer that handles spatial and temporal information separately, limiting the modeling of complex inter-variable dependencies; (d) graph-based methods have demonstrated strong performance in forecasting tasks but remain largely unexplored for generation.
3. Key Challenge: Time series exhibit rich temporal dependency structures (short-, medium-, and long-term periodicity), yet existing generative methods operate solely in the raw data domain without modeling these dependencies from a structural perspective.
4. Goal: To unify the modeling of temporal dependencies and structural relationships in time series from a graph perspective, enabling high-fidelity synthetic time series generation.
5. Key Insight: Treating time steps as graph nodes, constructing edges via Fourier spectral features to encode periodic dependencies, and performing diffusion modeling in the graph latent space.
6. Core Idea: Fourier transforms are used to discover periodic patterns in time series for graph construction; diffusion-based generation is then conducted in the graph latent representation space, with a topological fidelity metric employed to assess generation quality.

Method

Overall Architecture

TSGDiff proceeds in three stages: (1) Graph Construction and Encoding — time series are segmented via sliding windows and instance-normalized, Fourier transforms extract periodicity information to build dynamic graphs, and a GNN encoder produces latent representations; (2) Latent Diffusion Modeling — a diffusion–denoising process is executed in the latent graph space; (3) Graph Decoding — denoised latent representations are decoded back into synthetic time series.

Key Designs

1. Fourier-based Graph Construction:

   • Function: Converts time series into graph structures that encode periodic dependencies.
   • Mechanism: A discrete Fourier transform \(\tilde{X}_i^{(p)} = \sum_{n=0}^{w-1} \tilde{x}_{i+n} \cdot e^{-j\frac{2\pi}{w}pn}\) is applied to each window segment \(\tilde{X}_i\); the top-3 frequencies with the highest amplitudes are identified and converted to their corresponding periods. Nodes represent time steps; edges connect adjacent time steps and periodic neighbors. The adjacency matrix entry \(\mathbf{A}_{ij}=1\) indicates a temporal or periodic connection.
   • Design Motivation: The Fourier spectrum naturally reveals the periodic structure of time series; defining edges via periodicity simultaneously encodes short-, medium-, and long-term dependency patterns.

2. Graph VAE Encoder-Decoder:

   • Function: Encodes graph structures into latent representations and reconstructs them from latent vectors.
   • Mechanism: The encoder stacks multiple GCN layers (graph convolution \(y' = \text{Mish}(\text{BN}((W\mathbf{A}\tilde{X}+b)^T)^T)\) with residual connections), applies mean pooling, and outputs \(\mu\) and \(\log\sigma\); a latent vector is sampled via the reparameterization trick as \(z = \mu + \epsilon \odot \exp(\log\sigma / 2)\). The decoder recovers node features through fully connected layers with Tanh activation. A KL divergence loss \(\mathcal{L}_{KL}\) constrains the latent distribution toward a standard normal.
   • Design Motivation: GCN naturally aggregates information using the adjacency-matrix-defined graph structure; the VAE framework provides a regularized latent space.

3. Latent Diffusion + Topo-FID Metric:

   • Function: Performs generative modeling in the latent graph space; evaluates the structural fidelity of generated time series.
   • Mechanism: The forward process gradually adds noise as \(z_k = \sqrt{\alpha_k} \cdot z + \sqrt{1-\alpha_k} \cdot \epsilon\); the reverse process uses an MLP network to predict denoising, taking \(\text{concat}(z_k, t_{emb})\) as input. Topo-FID is defined as \(\alpha \cdot S_{edit} + (1-\alpha) \cdot S_{entropy}\), where \(S_{edit}\) measures adjacency matrix discrepancy and \(S_{entropy}\) compares structural entropy differences in node degree distributions.
   • Design Motivation: Performing diffusion in the latent space is more efficient than in the raw data domain and preserves structural consistency; conventional metrics cannot capture the structural characteristics of time series, and Topo-FID fills this gap from a graph perspective.

Loss & Training

The total loss function is: $\(\mathcal{L} = \mathcal{L}_{recon} + \beta \mathcal{L}_{KL} + \gamma \mathcal{L}_{denoising} + \delta \mathcal{L}_{Fourier}\)$

• \(\mathcal{L}_{recon}\): MSE reconstruction loss between input and decoder output.
• \(\mathcal{L}_{KL}\): KL divergence regularization (\(\beta=0.2\)).
• \(\mathcal{L}_{denoising}\): Diffusion denoising loss \(\|\epsilon - \epsilon_\theta(z_k, k)\|^2\) (\(\gamma=1\)).
• \(\mathcal{L}_{Fourier}\): Frequency-domain consistency loss \(\|\text{FFT}(x_0) - \text{FFT}(\hat{x}_0)\|^2\) (\(\delta=1\)).

Training configuration: batch size 128, learning rate 0.01, 500 epochs, sliding window size 48, stride 1.

Key Experimental Results

Main Results

Dataset	Metric	TSGDiff	Diffusion-TS	TimeGAN	Gain
ETTh	Topo-FID↑	0.986	0.864	0.798	+12.2%
Weather	Context-FID↓	0.353	1.161	2.420	-69.6%
EEG	Discriminative↓	0.301	0.492	0.391	-23.0%
ETTh	Predictive↓	0.020	0.026	0.030	-23.1%
Stocks	Correlational↓	0.026	0.027	0.061	-3.7%
Wind	Topo-FID↑	0.869	0.819	0.824	+5.0%

The average Discriminative score improves by 50% across 6 datasets.

Ablation Study

Configuration	Topo-FID↑	Context-FID↓	Discriminative↓	Note
w/o KL	0.787	44.467	0.500	Unconstrained latent space collapses
w/o Denoising	0.908	3.922	0.432	Limited generative capacity
w/o Fourier	0.883	0.407	0.061	Loss of frequency-domain information
Full (TSGDiff)	0.986	0.224	0.056	All components synergistically optimal

Key Findings

• The KL divergence loss is critical — removing it causes Context-FID to surge from 0.224 to 44.467, indicating complete latent space collapse.
• The Fourier loss has a significant impact on Topo-FID (0.986 → 0.883), demonstrating that frequency-domain constraints are essential for preserving structural fidelity.
• Kernel density estimation visualizations show that TSGDiff-generated distributions more closely match the real data distribution than those of Diffusion-TS.

Highlights & Insights

• Perspective Innovation: This is the first work to approach time series generation from a purely graph-based perspective, modeling temporal dependencies as graph edges — a meaningful paradigm shift.
• Natural Fusion of Fourier and Graph: Using Fourier spectral analysis to discover periodicity for constructing graph edges is more physically meaningful than manually defined or fully connected graphs.
• Novel Topo-FID Metric: Conventional metrics (FID, Discriminative score, etc.) cannot assess the structural properties of time series; Topo-FID addresses this gap.
• Unified Framework: The three-stage design of graph construction + graph VAE + latent diffusion unifies structural modeling and the generative process within a single framework.

Limitations & Future Work

• Graph construction considers only the top-3 frequency periodicities, potentially overlooking important non-periodic or nonlinear dependencies.
• Fourier transforms are applied independently per variable for edge construction, leaving cross-variable dependencies unmodeled explicitly (nodes represent time steps rather than variables).
• The latent diffusion network uses a simple MLP, which may limit the modeling capacity for complex latent distributions.
• Topo-FID still relies on pairwise comparison with real data, which may not fully capture generation diversity.
• The sliding window size is fixed at 48; sequences at different temporal scales may require adaptive window configurations.

Related Work & Insights

• vs. Diffusion-TS: Diffusion-TS performs diffusion in the raw data domain with seasonal-trend decomposition, processing spatial and temporal information separately; TSGDiff unifies modeling in the graph latent space, enabling better capture of structural dependencies.
• vs. TimeGAN: TimeGAN captures temporal dynamics via joint optimization of supervised and adversarial objectives, but is prone to mode collapse; TSGDiff's graph VAE + diffusion design avoids this issue.
• vs. FourierGNN (forecasting): FourierGNN combines Fourier and graph methods for forecasting tasks but has not been applied to generation; TSGDiff successfully extends this idea to the generative setting.

Rating

• Novelty: ⭐⭐⭐⭐ The graph-based perspective on time series generation is novel, and the Topo-FID metric constitutes a valuable contribution.
• Experimental Thoroughness: ⭐⭐⭐⭐ Comprehensive evaluation across 6 datasets, 5 metric categories, 4 baselines, ablation studies, and visualizations.
• Writing Quality: ⭐⭐⭐⭐ Architecture diagrams are clear and mathematical notation is well-defined, though some derivations could benefit from greater detail.
• Value: ⭐⭐⭐⭐ Introduces a new modeling paradigm and evaluation metric for time series generation with strong inspirational value.

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