Research map / Time series / Long-term forecasting
TARFVAE: Efficient One-Step Generative Time Series Forecasting via TARFLOW based VAE
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Proposes TARFVAE, a conditional VAE with a TARFLOW (Transformer autoregressive flow) posterior refinement and MLP modules, enabling one-step generative long-term time series forecasting using only the forward flow at inference.
Problem
Generative time series forecasting methods are slow (multi-step denoising or autoregressive decoding) and have mostly been evaluated only on short horizons, leaving their long-term accuracy and practical advantages unclear relative to deterministic models.
Approach
Adds a TARFLOW module to a conditional VAE to refine the Gaussian posterior into a more expressive latent distribution during training, while inference uses only the prior sample and VAE decoder, so full-horizon forecasts are generated in one step without autoregressive inverse flow operations.
Key results
- Achieves average MSE 0.355 on ETTh2 and 0.239 on Weather (horizon-averaged, L=96, 200 samples), best among listed deterministic baselines on 33 of 40 MSE entries.
- One-step generation takes about 3 ms per forecast on ETTh1 regardless of sample count, versus 8.3 to 21.6 ms for mr-Diff and 870 to 6724 ms for TimeGrad; reduces inference time 85.6% vs mr-Diff at H=720.
- Ablation: removing TARFLOW raises average MSE from 0.301 to 0.332 (about 10.3% worse).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add TARFLOW to VAE (ablation) | TARFVAE · All datasets (average) | MSE: 0.332 -> 0.301 | Helped |
| Add TARFLOW to VAE (ablation) | TARFVAE · All datasets (average) | MAE: 0.343 -> 0.333 | Helped |
| Use TARFLOW without VAE (ablation) | TARFVAE · All datasets (average) | MSE: 0.334 -> 0.301 | Helped |
| Use TARFLOW without VAE (ablation) | TARFVAE · All datasets (average) | MAE: 0.349 -> 0.333 | Helped |
| Increase inference sample count from 20 to 200 (ablation) | TARFVAE · All datasets (average) | MSE: 0.442 -> 0.427 | Helped |
| Increase inference sample count from 20 to 200 (ablation) | TARFVAE · All datasets (average) | CRPS: 0.369 -> 0.357 | Helped |
| Replace DUET with TARFVAE | multivariate forecasting · ETTh2 (Avg) | MSE: 0.372 -> 0.355 | Helped |
| Replace DUET with TARFVAE | multivariate forecasting · Weather (Avg) | MSE: 0.251 -> 0.239 | Helped |
| Replace DUET with TARFVAE | multivariate forecasting · Exchange (Avg) | MSE: 0.318 -> 0.349 | Hurt |
| Replace DUET with TARFVAE | multivariate forecasting · Electricity (Avg) | MAE: 0.259 -> 0.264 | Hurt |
| Use one-step TARFVAE generation instead of mr-Diff | ETTh1 forecasting at H=720 · ETTh1 | inference time (ms): 21.6 -> 3.0 | Helped |
| Use TARFVAE instead of probabilistic baselines | forecasting under the ProbTS CRPS protocol · Weather, prediction length 192 | CRPS: 0.068 -> 0.070 | Hurt |
Surprising findings
- Simple MLP modules with a flow-refined VAE match or beat Transformer-based deterministic SOTA on most benchmarks, supporting the claim that complex temporal architectures may be unnecessary.
Limitations
- Encoder, decoder, and prior all use identical simple MLP blocks, which may limit forecasting performance.
- MLP blocks may not extract complex temporal patterns as well as more advanced temporal modules.
- Some generative baselines (mr-Diff, TimeDiff) are not open-sourced, so inference efficiency comparisons rely on reruns or reported numbers.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Exchange Weather Solar-Energy
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Exchange Weather Solar
Metrics: MSE MAE CRPS inference time
Baselines: DUET SOFTS iTransformer TSMixer PatchTST Crossformer TiDE DLinear FEDformer mr-Diff TimeDiff TimeGrad
Builds on: TARFLOW variational autoencoder Real NVP conditional VAE mr-Diff
Closest papers by meaning
- $K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting (ICML 2025 · similarity 0.88)
- Time Series Generation Under Data Scarcity: A Unified Generative Modeling Approach (NeurIPS 2025 · similarity 0.88)
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- HDT: Hierarchical Discrete Transformer for Multivariate Time Series Forecasting (AAAI 2025 · similarity 0.87)
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