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Population Aware Diffusion for Time Series Generation
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Proposes PaD-TS, a diffusion model for time series generation that adds a population-aware MMD loss on cross-correlation distributions (with same-diffusion-step sampling) and a dual-channel transformer/DiT architecture to better preserve population-level properties.
Problem
Diffusion-based time series generators preserve individual-level authenticity but drift in population-level properties such as per-dimension value distributions and cross-dimension functional dependencies (e.g., cross-correlation).
Approach
Adds an MMD-based population loss on cross-correlation distributions computed over mini-batches where all samples share the same diffusion step (same diffusion step sampling), plus a dual-channel encoder that processes temporal and cross-dimensional information separately with DiT blocks.
Key results
- Averaged over Sines, Stocks, Energy at length 24, PaD-TS improves FDDS by 5.9x and VDS by 5.7x over Diffusion-TS while keeping comparable discriminative accuracy.
- On Energy with lengths 64-256, PaD-TS improves FDDS by 6.1x on average and DA by 3.4x on average over the best baseline.
- On Stocks, PaD-TS is worse than Diffusion-TS on several feature-based metrics (e.g., ACD 0.111 vs 0.028, KD 4.290 vs 2.207).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PaD-TS instead of Diffusion-TS | Time-series generation · Sines, Stocks, and Energy | FDDS: improves the FDDS score by 5.9x | Helped |
| Use PaD-TS instead of Diffusion-TS | Time-series generation · Sines, Stocks, and Energy | VDS: improves the VDS score by 5.7x | Helped |
| Add a temporal channel (ablation) | PaD-TS · Sines, Stocks, and Energy | FDDS: 0.0005, 1.8838, 0.5254 vs 0.0003, 0.0588, 0.0442 | Helped |
| Add a dimension channel (ablation) | PaD-TS · Sines, Stocks, and Energy | FDDS: 0.0087, 0.0868, 0.0533 vs 0.0003, 0.0588, 0.0442 | Helped |
| Add the PAT objective (ablation) | PaD-TS · Sines, Stocks, and Energy | FDDS: 0.0007, 0.2459, 0.0816 vs 0.0003, 0.0588, 0.0442 | Helped |
| Add the SSS strategy (ablation) | PaD-TS · Sines, Stocks, and Energy | FDDS: 0.0286, 0.0965, 0.3626 vs 0.0003, 0.0588, 0.0442 | Helped |
| Increase the PAT loss weight α (ablation) | PaD-TS · Energy | VDS | Hurt |
| Increase the PAT loss weight α (ablation) | PaD-TS · Energy | FDDS | Helped |
| Set α to 0.05 (ablation) | PaD-TS · Energy | VDS: α=0.05 | Hurt |
| Set α to 0.05 (ablation) | PaD-TS · Energy | FDDS: α=0.05 | Hurt |
Surprising findings
- Training time for PaD-TS is roughly 2-5x longer than Diffusion-TS (e.g., Energy 117 min vs 60 min).
- Large alpha (0.05) causes training collapse with large VDS and FDDS scores.
Limitations
- Training is noticeably slower than Diffusion-TS due to the pairwise population loss and same-step sampling.
- Mixed results on feature/distance metrics; PaD-TS is not uniformly better (e.g., Stocks ACD and KD).
- Population loss weight alpha is sensitive; large values collapse training.
Experimental setup
Datasets: Sines Stocks Energy Mujoco fMRI
Benchmarks: Sines Stocks Energy Mujoco fMRI
Metrics: VDS FDDS discriminative accuracy predictive score MDD ACD SD KD ED DTW
Baselines: Diffusion-TS TimeGAN TimeVAE
Builds on: Diffusion-TS InfoVAE improved DDPM diffusion transformer (DiT)
Closest papers by meaning
- Retrieval-Augmented Diffusion Models for Time Series Forecasting (NeurIPS 2024 · similarity 0.88)
- Auto-Regressive Moving Diffusion Models for Time Series Forecasting (AAAI 2025 · similarity 0.88)
- FIDE: Frequency-Inflated Conditional Diffusion Model for Extreme-Aware Time Series Generation (NeurIPS 2024 · similarity 0.88)
- Diffusion-TS: Interpretable Diffusion for General Time Series Generation (ICLR 2024 · similarity 0.87)
- ANT: Adaptive Noise Schedule for Time Series Diffusion Models (NeurIPS 2024 · similarity 0.87)
- Time Series Generation Under Data Scarcity: A Unified Generative Modeling Approach (NeurIPS 2025 · similarity 0.87)
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