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Diffusion-TS: Interpretable Diffusion for General Time Series Generation
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Proposes Diffusion-TS, a non-autoregressive DDPM for multivariate time series generation that uses an encoder-decoder transformer with interpretable trend and Fourier seasonality decomposition, a Fourier-augmented reconstruction loss, and reconstruction-guided sampling for conditional tasks.
Problem
Generating high-quality multivariate time series with diffusion models while preserving interpretable temporal structure (trend, seasonality) and handling long sequences, unconditional and conditional tasks.
Approach
Diffusion model whose transformer decoder has interpretable trend (polynomial regressor) and Fourier seasonal synthesis layers, trained to predict the clean sample x0 directly with an added FFT-domain loss; conditional generation via reconstruction-based gradient guidance without retraining.
Key results
- Diffusion-TS achieves best Context-FID on Sines (0.006), Stocks (0.147 second-best vs TimeGAN 0.103), ETTh (0.116) and MuJoCo (0.013), Energy (0.089), fMRI (0.105) in the 24-length setting.
- Diffusion-TS reduces discriminative score on all six datasets, e.g. fMRI 0.167 vs 0.245 for next-best DiffTime, averaging roughly 50% improvement claimed.
- On Solar forecasting Diffusion-TS reaches MSE 3.75e2 versus 5.03e2 for SSSD; on MuJoCo imputation at 70% missing it gets 0.37e-3 vs CSDI 0.24e-3 (CSDI better at 70%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add Fourier-based training loss (ablation) | Diffusion-TS · 24-step generation across Sines, Stocks, ETTh, MuJoCo, Energy, and fMRI | Context-FID: 0.008±.001 -> 0.006±.000 (Sines); 0.216±.031 -> 0.147±.025 (Stocks); 0.219±.021 -> 0.116±.010 (ETTh); 0.017±.002 -> 0.01 | Helped |
| add seasonal-trend decomposition (ablation) | Diffusion-TS · 24-step generation across Sines, Stocks, ETTh, MuJoCo, Energy, and fMRI | Context-FID: 0.008±.000 -> 0.006±.000 (Sines); 0.181±.029 -> 0.147±.025 (Stocks); 0.121±.004 -> 0.116±.010 (ETTh); 0.018±.002 -> 0.01 | Helped |
| use transformer encoder and self-attention instead of convolutional network (ablation) | Diffusion-TS · 24-step generation across six datasets | Context-FID: 0.007±.000 -> 0.006±.000 (Sines); 0.254±.024 -> 0.147±.025 (Stocks); 0.229±.024 -> 0.116±.010 (ETTh); 0.040±.003 -> 0.01 | Mixed |
| predict clean signal instead of diffusion noise (ablation) | Diffusion-TS · 24-step generation across six datasets | Context-FID: 0.019±.004 -> 0.006±.000 (Sines); 0.215±.033 -> 0.147±.025 (Stocks); 0.265±.008 -> 0.116±.010 (ETTh); 0.017±.001 -> 0.01 | Helped |
| include Residual, Season, and Trend components together (ablation) | Diffusion-TS · MuJoCo imputation at 70%, 80%, and 90% missing | MSE: 0.51(1), 0.45(5), 0.46(2), 0.63(3) -> 0.37(3) (70%); 0.59(7), 0.52(3), 0.50(5), 1.05(6) -> 0.43(3) (80%); 0.85(10), 0.77 | Helped |
| increase or decrease guidance strength from γ=5e-2 (ablation) | Diffusion-TS conditional sampling · MuJoCo imputation at 70%, 80%, and 90% missing | MSE: γ=1e-1: 0.37(4), 0.45(0), 0.82(9); γ=1.: 2.8(13), 4.1(10), 6.8(17); γ=1e-2: 0.60(5), 0.70(10), 1.07(14); γ=1e-3: 3.1(8), | Mixed |
Surprising findings
- Removing the transformer (convolutional-only variant) hurts performance most on Energy, while on fMRI an interpretability-only network performs best on some metrics.
- Diffusion-TS slightly underperforms CSDI on MuJoCo imputation at 70% missing ratio.
Limitations
- High inference cost of DDPM sampling compared with GAN-based approaches.
- Discriminative and predictive scores not uniformly best; CSDI better on MuJoCo imputation at 70% missing.
- Hyperparameter tuning was limited.
Experimental setup
Datasets: Stocks ETTh Energy fMRI Sines MuJoCo Solar
Benchmarks: Sines Stocks ETTh MuJoCo Energy fMRI Solar MuJoCo imputation
Metrics: Context-FID score Correlational score Discriminative score Predictive score MSE
Baselines: TimeGAN TimeVAE Diffwave DiffTime Cot-GAN CSDI SSSD TLAE
Builds on: DDPM CSDI N-BEATS Diffwave
Closest papers by meaning
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- TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation (ICML 2025 · similarity 0.89)
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