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A Non-isotropic Time Series Diffusion Model with Moving Average Transitions
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Proposes MA-TSD, a non-isotropic time series diffusion model whose forward process uses moving-average (low-pass) transitions, yielding a DDIM-style accelerable backward process that doubles as time series super-resolution.
Problem
Standard isotropic DDPM applied to time series degrades low-frequency information too rapidly, causing gradient contradictions and unstable training; existing time series diffusion models inherit this design.
Approach
Replace the isotropic Gaussian forward process with a non-Markovian forward process whose transition matrices are moving-average low-pass filters with increasing kernel sizes, plus a dataset-based noise schedule, instance normalization, and a factor-based accelerated backward sampler that enables super-resolution via the backward process.
Key results
- On forecasting averaged over horizons, MA-TSD achieves the best average MSE on 6/6 datasets (e.g., Electricity 0.3404 vs. TMDM 0.4071) and ranks first on average.
- On super-resolution (e.g., MFRED 3x), MA-TSD reaches Consistency 0.0032 and Context-FID 0.1047 versus DDPM 0.0291/3.1028 and FM-VP 0.0328/1.3481.
- Ablation on Context-FID shows that removing both MA and IN gives the worst results (e.g., MFRED 29.71), while combining both gives the best (2.67).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use moving-average transitions and instance normalization instead of direct DDIM on raw time series (ablation) | MA-TSD · MFRED, Wind, Solar synthesis | Context-FID: 29.7093 -> 2.6742; 52.3499 -> 16.9026; 43.6236 -> 8.0297 | Helped |
| Add instance normalization without moving-average transitions (ablation) | MA-TSD · MFRED, Wind, Solar synthesis | Context-FID: 29.7093 -> 13.1704; 52.3499 -> 44.6908; 43.6236 -> 35.3704 | Helped |
| Add moving-average transitions without instance normalization (ablation) | MA-TSD · MFRED, Wind, Solar synthesis | Context-FID: 29.7093 -> 4.9403; 52.3499 -> 21.3606; 43.6236 -> 8.0744 | Helped |
| Use factor-only backward-step selection instead of random or uniform selection (ablation) | MA-TSD · MFRED, Wind, Solar synthesis | Context-FID | Helped |
| Use MA-TSD rather than diffusion forecasting baselines | Time series forecasting · Electricity, ETTh2, ETTm2, Exchange, Traffic, Weather | MSE: 0.3404 vs 0.4071; 0.2121 vs 0.2172; 0.1241 vs 0.1700; 0.3718 vs 0.4801; 0.1660 vs 0.1805; 0.2074 vs 0.1938 | Mixed |
| Use MA-TSD rather than diffusion forecasting baselines | Time series forecasting · Electricity, ETTh2, ETTm2, Exchange, Traffic, Weather | CRPS: 0.1747 vs 0.1881; 0.1567 vs 0.1591; 0.1135 vs 0.1253; 0.2178 vs 0.2117; 0.1156 vs 0.1076; 0.1501 vs 0.1261 | Mixed |
| Use MA-TSD instead of conditional DDPM or FM-VP | Time series super-resolution · MFRED, Wind, Solar at 3×, 6×, and 12× | Consistency: Table 3: MA-TSD consistency is lower than both benchmarks at all reported scales and datasets | Helped |
| Use MA-TSD instead of conditional DDPM or FM-VP | Time series super-resolution · MFRED, Wind, Solar at 3×, 6×, and 12× | Context-FID: Table 3: MA-TSD Context-FID is lower except Solar at 6× and 12× versus FM-VP | Mixed |
Surprising findings
- The paper reports that MA (moving-average schedule) contributes more than instance normalization to the performance gains.
Limitations
- Improvement on the Weather dataset is marginal, attributed to high-resolution data where high-frequency components matter.
- Forecasting backbone is a simple MLP-based denoiser; SOTA architectures not integrated.
- Non-overlapping moving average kernels require kernel sizes that are factors of the series length, and the framework is evaluated on relatively few datasets.
Experimental setup
Datasets: Electricity ETTh2 ETTm2 Exchange Traffic Weather MFRED Wind Solar ECG
Benchmarks: Electricity ETTh2 ETTm2 Exchange Traffic Weather MFRED Wind Solar ECG
Metrics: MSE CRPS Consistency Context-FID Discriminative score Predictive score
Baselines: CSDI SSSD D3VAE TMDM MR-Diff DDPM FM-VP KoVAE ImagenTime Autoformer Non-stationary Transformer PatchTST
Builds on: DDPM DDIM Blurring Diffusion Models TMDM mr-diff
Closest papers by meaning
- Auto-Regressive Moving Diffusion Models for Time Series Forecasting (AAAI 2025 · similarity 0.91)
- Diffusion-TS: Interpretable Diffusion for General Time Series Generation (ICLR 2024 · similarity 0.89)
- Retrieval-Augmented Diffusion Models for Time Series Forecasting (NeurIPS 2024 · similarity 0.89)
- MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process (ICLR 2024 · similarity 0.88)
- Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction (NeurIPS 2025 · similarity 0.88)
- Time Series Diffusion in the Frequency Domain (ICML 2024 · similarity 0.88)
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