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Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series
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Transforms time series into images (delay embedding or STFT) and trains an EDM diffusion model on them, enabling unconditional, interpolation and extrapolation generation across short to ultra-long sequences.
Problem
Generative modeling of time series spans short multivariate sequences and long or ultra-long univariate sequences, but existing methods typically handle only one regime, due to RNN gradient issues, transformer quadratic cost, and limited SSM expressivity.
Approach
Map time series to small images with invertible transforms (delay embedding, STFT) and apply a vision diffusion backbone (EDM), so one framework scales from length 24 to about 17.5k without architectural changes.
Key results
- Short unconditional generation: on MuJoCo the method improves the second-best discriminative and predictive scores by about 88% and 21% (disc .007 vs .059 for DiffTime).
- Ultra-long unconditional generation on KDD-Cup yields predictive score .001 versus LS4's second-best .049.
- Interpolation on Physionet MSE .004 (x10^-3) versus .620 for LS4, with improvements of two orders of magnitude over baselines on long interpolation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ImagenTime instead of the strongest listed baseline | Short-term unconditional generation · MuJoCo | disc: .059 ± .009 -> .007 ± .005 | Helped |
| Use ImagenTime instead of the strongest listed baseline | Long-term unconditional generation · FRED-MD | pred: .037 -> .009 | Helped |
| Use ImagenTime instead of LS4 | Long-term unconditional generation · NN5 Daily | pred: .241 -> .393 | Hurt |
| Use ImagenTime instead of LS4 | Long-term unconditional generation · Temp Rain | marg: .083 -> .409 | Hurt |
| Use ImagenTime instead of LS4 | Ultra-long unconditional generation · KDD-Cup | pred: .049 -> .001 | Helped |
| Use delay embedding rather than folding (ablation) | ImagenTime · FRED-MD | marg: .012 -> .017 | Hurt |
| Use STFT rather than delay embedding (ablation) | ImagenTime · FRED-MD | pred: .021 -> .009 | Helped |
| Use delay embedding rather than STFT (ablation) | ImagenTime · Energy | disc: .271 -> .040 | Helped |
| Use GAF rather than delay embedding (ablation) | ImagenTime · Energy | disc: .040 -> .349 | Hurt |
Surprising findings
- Gramian angular field transform does not scale to long sequences because image size grows linearly with series length.
Limitations
- Requires slightly higher computational resources than prior methods.
- Marginal score on Temp Rain is inferior, attributed to frequent zero values in the data.
- Several results are inferior, e.g., NN5 Daily pred and Temp Rain marg.
Experimental setup
Datasets: Stocks Energy MuJoCo Sine FRED-MD NN5 Daily Temp Rain Traffic KDD-Cup ETTh1 ETTh2 ETTm1
Benchmarks: Stocks Energy MuJoCo FRED-MD NN5 Daily Temp Rain Traffic KDD-Cup ETTh1 ETTh2 ETTm1 ETTm2
Metrics: discriminative score predictive score marginal score classification score MSE Wasserstein distance
Baselines: KoVAE DiffTime GT-GAN TimeGAN RCGAN C-RNN-GAN T-Forcing P-Forcing WaveNet WaveGAN LS4 SaShiMi
Builds on: EDM LS4 delay embedding short-time Fourier transform
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