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ANT: Adaptive Noise Schedule for Time Series Diffusion Models
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Proposes ANT, a method that selects a per-dataset noise schedule for time series diffusion models by scoring how linearly each candidate schedule reduces the non-stationarity (IAAT) of the data, with no training needed.
Problem
Time series diffusion models usually reuse noise schedules from other domains (e.g., linear schedule with T=100), which ignores time-series characteristics and yields suboptimal forecasting, refinement, and generation performance.
Approach
Define the ANT score from a dataset's integrated absolute autocorrelation time (IAAT) under each candidate schedule: prefer schedules whose non-stationarity curve decreases linearly over steps, collapses to noise at the final step, and uses many steps. Scores are computed offline, so no model training is needed to select the schedule.
Key results
- TSDiff+ANT reduces average CRPS across eight forecasting datasets from 0.166 to 0.150 (about 9.5% improvement) and gains up to 27.8% on M4.
- In refinement, TSDiff with ANT improves CRPS on all seven reported datasets, e.g., +25.0% on Exchange and +14.4% on UberTLC.
- ANT-selected schedules match the oracle on several datasets and keep the forecasting gain when T is constrained to 50 steps or fewer.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Select an adaptive noise schedule with ANT instead of the shared linear schedule | TSDiff · Forecasting across eight datasets | CRPS: +22.4%; +4.1%; +3.9%; +25.1%; +27.8%; +5.2%; +3.0%; +6.8% | Helped |
| Add diffusion step embedding to a linear-schedule model (ablation) | TSDiff+ANT · Solar forecasting | CRPS: 0.326 -> 0.399 | Hurt |
| Add diffusion step embedding to a linear-schedule model (ablation) | TSDiff+ANT · Traffic forecasting | CRPS: 0.101 -> 0.098 | Helped |
| Add diffusion step embedding to a cosine-schedule model (ablation) | TSDiff+ANT · Exchange forecasting | CRPS: 0.010 -> 0.009 | Helped |
| Add diffusion step embedding to a cosine-schedule model (ablation) | TSDiff+ANT · Electricity forecasting | CRPS: 0.050 -> 0.047 | Helped |
| Add diffusion step embedding to a cosine-schedule model (ablation) | TSDiff+ANT · Wikipedia forecasting | CRPS: 0.206 -> 0.206 | No clear effect |
| Add diffusion step embedding to a cosine-schedule model (ablation) | TSDiff+ANT · M4 forecasting | CRPS: 0.052 -> 0.026 | Helped |
| Replace TSDiff's shared linear schedule with ANT-selected schedules | TSDiff · Forecasting, 8 datasets | Average CRPS: 0.166 -> 0.150 | Helped |
| Use IAAT rather than LagAC or VarAC to select schedules (ablation) | TSDiff+ANT · Forecasting, 8 datasets | Average CRPS: 0.158; 0.151; 0.150 | Helped |
| Use the AUC discrepancy metric rather than alternatives to select schedules (ablation) | TSDiff+ANT · Forecasting, 8 datasets | Average CRPS: 0.152; 0.151; 0.151; 0.152; 0.150 | Helped |
| Use a cosine schedule instead of a shared linear schedule | TSDiff · Forecasting, 8 datasets | Average CRPS: 0.166 -> 0.160 | Helped |
| Use ANT rather than a zero-terminal-SNR schedule | TSDiff · Forecasting, 8 datasets | Average CRPS: 0.185 -> 0.150 | Helped |
Surprising findings
- Larger diffusion step count T is not always better for time series: the best oracle performance on UberTLC is at T=20.
- Diffusion step embedding is unnecessary (and harmful in most cases) when a linear noise schedule is used, since step information is inherent in the noisy data.
Limitations
- Searches only over 35 candidate schedules from linear, cosine, and sigmoid families; it does not find the optimal schedule itself.
- Experiments use only univariate datasets from GluonTS with TSDiff as the backbone.
Experimental setup
Datasets: Solar Electricity Traffic Exchange M4 UberTLC KDDCup Wikipedia
Benchmarks: Solar Electricity Traffic Exchange M4 UberTLC KDDCup Wikipedia
Metrics: CRPS
Baselines: DeepAR DeepState Transformer TFT CSDI TSDiff TimeGAN TimeVAE Cosine schedule Zero terminal SNR schedule
Builds on: TSDiff DDPM integrated autocorrelation time improved noise schedule (cosine)
Closest papers by meaning
- DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting (NeurIPS 2026 · similarity 0.89)
- Non-stationary Diffusion For Probabilistic Time Series Forecasting (ICML 2025 · similarity 0.88)
- Auto-Regressive Moving Diffusion Models for Time Series Forecasting (AAAI 2025 · similarity 0.88)
- Probabilistic Time Series Modeling with Decomposable Denoising Diffusion Model (ICML 2024 · similarity 0.87)
- Retrieval-Augmented Diffusion Models for Time Series Forecasting (NeurIPS 2024 · similarity 0.87)
- Population Aware Diffusion for Time Series Generation (AAAI 2025 · similarity 0.87)
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