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Auto-Regressive Moving Diffusion Models for Time Series Forecasting
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Proposes ARMD, an unconditional diffusion model for time series forecasting that treats future and historical series as the start and end states of a deterministic sliding-based diffusion chain, with a linear devolution network.
Problem
Existing diffusion-based time series forecasting models treat forecasting as noise-based conditional generation, which misaligns the diffusion process with the continuous sequential nature of the TSF objective and discards intermediate series information.
Approach
Replace Gaussian noising with deterministic sliding of the series: the future series is the initial diffusion state and the historical series the final state, with intermediate states obtained by sliding the window; a linear devolution network with a distance-based, time-step-weighted output predicts the evolution trend, and sampling starts from history without conditioning.
Key results
- ARMD achieves the best MSE/MAE in 12 of 14 settings against diffusion-based TSF baselines (Table 1).
- On ETTm1, ARMD reduces MSE by 47.7% and MAE by 30.1% relative to the second-best model D3VAE.
- ARMD trains and infers more than tenfold faster than Diffusion-TS, MG-TSD and TimeGrad on ETTm1 (training 11.872 s vs 149.974 s for Diffusion-TS; inference 31.650 s vs 1183.593 s).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use ARMD instead of diffusion-based TSF baselines | multivariate time-series forecasting · Solar Energy, ETTh1, ETTm1, Exchange, Stock | MSE | Helped |
| replace sliding intermediate-state generation with interpolation (ablation) | ARMD · seven forecasting datasets | MSE | Hurt |
| replace distance-based devolution with t-embedding (ablation) | ARMD · seven forecasting datasets | MSE | Hurt |
| replace linear devolution backbone with Transformer (ablation) | ARMD · seven forecasting datasets | MSE | Mixed |
| add deviations to intermediate states during training (ablation) | ARMD · seven forecasting datasets | MSE | Helped |
| add noise during sampling (ablation) | ARMD · seven forecasting datasets | MSE | Hurt |
Surprising findings
- A Transformer backbone in the devolution network performs worse than the linear backbone in 11 of 14 settings, and in Solar Energy it reaches MSE 1.343 versus 0.167 for ARMD.
- Adding sampling noise degrades performance, supporting the deterministic formulation.
Limitations
- Comparisons with non-diffusion baselines rely partly on numbers copied from iTransformer, and the Stock dataset was re-run with official implementations.
- Hyperparameters b, c, d are chosen by grid search, and the sampling steps are tuned on the validation set, adding tuning dependence.
- Only one historical and prediction length (96) is evaluated; the Transformer-backbone ablation shows large instability on Solar Energy.
Experimental setup
Datasets: Solar Energy Exchange Stock ETTh1 ETTh2 ETTm1 ETTm2
Benchmarks: Solar Energy ETTh1 ETTh2 ETTm1 ETTm2 Exchange Stock
Metrics: MSE MAE
Baselines: Diffusion-TS MG-TSD TSDiff D3VAE TimeGrad iTransformer TimesNet DLinear PatchTST Client
Builds on: DDPM DDIM ARMA iTransformer Diffusion-TS
Closest papers by meaning
- A Non-isotropic Time Series Diffusion Model with Moving Average Transitions (ICML 2025 · similarity 0.91)
- Retrieval-Augmented Diffusion Models for Time Series Forecasting (NeurIPS 2024 · similarity 0.90)
- Non-stationary Diffusion For Probabilistic Time Series Forecasting (ICML 2025 · similarity 0.90)
- MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process (ICLR 2024 · similarity 0.89)
- DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting (NeurIPS 2026 · similarity 0.89)
- Conditional Diffusion Model with Nonlinear Data Transformation for Time Series Forecasting (ICML 2025 · similarity 0.89)
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