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MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process
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Proposes MG-TSD, a multi-granularity diffusion model for probabilistic time series forecasting that uses coarse-grained versions of the series as targets at intermediate diffusion steps to guide training.
Problem
Diffusion models for probabilistic time series forecasting are unstable due to stochastic sampling, producing diverse and sometimes low-fidelity samples that hurt forecast accuracy.
Approach
Treat coarse-grained (smoothed) versions of the series as guidance targets at intermediate diffusion steps, with a shared denoising network and partially shared variance schedules across granularities, so the forward diffusion mirrors fine-to-coarse smoothing; no external data or classifier labels are needed.
Key results
- MG-TSD achieves the lowest CRPS_sum on all six datasets, e.g., Solar 0.3081 vs TimeGrad 0.3335 and Electricity 0.0149 vs 0.0232.
- On Taxi, MG-TSD reaches CRPS_sum 0.1159 vs TimeGrad 0.1255; on Wikipedia 0.0529 vs 0.0555.
- Increasing the number of granularities from 2 to 4 improves Solar CRPS_sum from 0.3172 to 0.3081, with diminishing gains beyond 4-5 levels.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| introduce multi-granularity guided diffusion | TimeGrad · Solar, Electricity, Traffic, KDD-cup, Taxi, Wikipedia | CRPS_sum: Solar: 0.3335_{\pm 0.0653} -> 0.3081_{\pm 0.0099}; Electricity: 0.0232_{\pm 0.0035} -> 0.0149_{\pm 0.0017}; Traffic: 0.0 | Helped |
| increase the number of granularity levels from 2 to 4 (ablation) | MG-TSD · Solar | CRPS_sum: 0.3172_{\pm 0.0249} -> 0.3081_{\pm 0.0099} | Helped |
| increase the number of granularity levels from 2 to 4 (ablation) | MG-TSD · Electricity | CRPS_sum: 0.0174_{\pm 0.0042} -> 0.0149_{\pm 0.0017} | Helped |
| increase the number of granularity levels from 2 to 5 (ablation) | MG-TSD · Traffic | CRPS_sum: 0.0347_{\pm 0.0020} -> 0.0323_{\pm 0.0125} | Helped |
| increase the number of granularity levels from 2 to 5 (ablation) | MG-TSD · KDD-cup | CRPS_sum: 0.2427_{\pm 0.1167} -> 0.1837_{\pm 0.0636} | Helped |
| increase granularity levels from 4 to 5 (ablation) | MG-TSD · Solar and Electricity | CRPS_sum: Solar: 0.3081_{\pm 0.0099} -> 0.3093_{\pm 0.0411}; Electricity: 0.0149_{\pm 0.0017} -> 0.0153_{\pm 0.0027} | Hurt |
| set share ratio to 80% instead of 20% with 4-hour guidance (ablation) | MG-TSD · Solar | CRPS_sum: 0.3489_{\pm 0.0190} -> 0.3172_{\pm 0.0249} | Helped |
| increase share ratio from 80% to 100% with 4-hour guidance (ablation) | MG-TSD · Solar | CRPS_sum: 0.3172_{\pm 0.0249} -> 0.3178_{\pm 0.0342} | Hurt |
| set share ratio to 60% instead of 20% with 6-hour guidance (ablation) | MG-TSD · Solar | CRPS_sum: 0.3378_{\pm 0.0305} -> 0.3166_{\pm 0.0376} | Helped |
| increase share ratio from 60% to 100% with 6-hour guidance (ablation) | MG-TSD · Solar | CRPS_sum: 0.3166_{\pm 0.0376} -> 0.3232_{\pm 0.0396} | Hurt |
| set share ratio to 60% instead of 20% with 12-hour guidance (ablation) | MG-TSD · Solar | CRPS_sum: 0.3440_{\pm 0.0391} -> 0.3240_{\pm 0.0382} | Helped |
| set share ratio to 40% instead of 20% with 24-hour guidance (ablation) | MG-TSD · Solar | CRPS_sum: 0.3315_{\pm 0.0266} -> 0.3276_{\pm 0.0358} | Helped |
Surprising findings
- Direct ensembling of coarse-grained TimeGrad outputs (MG-Input) gives only marginal gains over TimeGrad, suggesting ensembling is inefficient compared with the proposed guidance.
- Coarser granularities (12h, 24h) yield smaller improvements, attributed to loss of local fluctuation information.
Limitations
- Performance depends on hyperparameters such as share ratio and loss weights, selected by a parameter search over tested choices.
- Gains diminish for very coarse granularities and for more than four to five granularity levels.
- Memory consumption grows linearly with the number of granularities.
Experimental setup
Datasets: Solar Electricity Traffic Taxi KDD-cup Wikipedia
Benchmarks: Solar Electricity Traffic Taxi KDD-cup Wikipedia
Metrics: CRPS_sum NMAE_sum NRMSE_sum
Baselines: Vec-LSTM ind-scaling GP-Scaling GP-Copula LSTM-MAF Transformer-MAF TimeGrad TACTiS MG-Input TimeDiff D3VAE PatchTST Autoformer
Builds on: TimeGrad DDPM classifier-free guidance
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