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Probabilistic Time Series Modeling with Decomposable Denoising Diffusion Model
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Problem
Existing SDE-based probabilistic time series models are hard to design (drift and diffusion coefficients are difficult to derive) and generate slowly, needing many sampling steps; attention-based backbones are quadratic and lack inductive bias.
Approach
Build generative models directly from the explicit solution of linear SDEs, decomposed into a signal dissipation term h(t) and a noise injection term l(t,W_t), which unifies DDMs and continuous flow models and allows fast 10-step sampling; the network combines damped EMA (an SSM) with time- and feature-oriented linear gated attention in a WaveNet.
Key results
- On PhysioNet imputation, D3M reduces RMSE by 4.6% (10% missing) and CRPS by 4.3% versus state-of-the-art baselines.
- D3M reduces inference time by up to 87.7% versus CSDI and uses 10 sampling steps versus CSDI's 50-100.
- On forecasting, D3M improves CRPSsum by 13.6% on Solar and 18.9% on Traffic, and is comparable to ScoreGrad on Electricity, Taxi and Exchange.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use D3M(Constant-Sqrt) rather than SSSD | Probabilistic imputation · Physionet, 10% missing | RMSE: 0.459±0.001 -> 0.438±0.003 | Helped |
| Use D3M(Constant-Linear) rather than SAITS | Probabilistic imputation · Air quality | RMSE: 18.68±0.13 -> 18.13±0.23 | Helped |
| Use D3M(Constant-Linear) rather than SSSD | Probabilistic imputation · Physionet, 50% missing | CRPS: 0.331±0.002 -> 0.325±0.002 | Helped |
| Use D3M(Constant-Linear) rather than SSSD | Probabilistic forecasting · Solar | CRPSsum: 0.241± 0.014 -> 0.208±0.018 | Helped |
| Use D3M(Constant-Sqrt) rather than ScoreGrad(VE SDE) | Probabilistic forecasting · Traffic | CRPSsum: 0.037±0.003 -> 0.030±0.002 | Helped |
| Use D3M(Constant-Linear) rather than ScoreGrad(VP SDE) | Probabilistic forecasting · Wikipedia | CRPSsum: 0.041±0.003 -> 0.047±0.003 | Hurt |
| Add EMA to time and feature gated attention (ablation) | D3M sequence modeling · Physionet, 50% missing | RMSE: 0.621 -> 0.615 | Helped |
| Add time gated attention to EMA and feature gated attention (ablation) | D3M sequence modeling · Physionet, 50% missing | RMSE: 0.628 -> 0.615 | Helped |
| Add feature gated attention to EMA and time gated attention (ablation) | D3M sequence modeling · Physionet, 50% missing | RMSE: 0.636 -> 0.615 | Helped |
| Add EMA, time gated attention, and feature gated attention (ablation) | D3M sequence modeling · Physionet, 50% missing | RMSE: 1.055 -> 0.615 | Helped |
Surprising findings
- Constant-type h(t) outperforms Linear-type h(t) on most imputation settings, suggesting the choice of signal dissipation matters more than noise injection choice.
- The learned coefficients from the signal loss do not guarantee the required constraints, requiring modified samplers.
Limitations
- Forecasting uses a reduced architecture (attention blocks removed) to save memory, and only the GRU features are used.
- Learned h(t) coefficients may violate the constraints, requiring modified samplers.
- Results on forecasting are only comparable, not superior, to ScoreGrad on several datasets.
Experimental setup
Datasets: PhysioNet Challenge 2012 Air quality Exchange Solar Electricity Traffic Taxi Wikipedia
Benchmarks: PhysioNet Challenge 2012 Air quality Exchange Solar Electricity Traffic Taxi Wikipedia
Metrics: RMSE CRPS CRPSsum
Baselines: CSDI CSBI SSSD TS-Diff SAITS TIDER TimeGrad ScoreGrad
Builds on: CSDI WaveNet ScoreSDE flow matching S4
Closest papers by meaning
- Diffusion-TS: Interpretable Diffusion for General Time Series Generation (ICLR 2024 · similarity 0.90)
- Non-stationary Diffusion For Probabilistic Time Series Forecasting (ICML 2025 · similarity 0.90)
- DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting (NeurIPS 2026 · similarity 0.89)
- Assessing the quality of denoising diffusion models in Wasserstein distance: noisy score and optimal bounds (NeurIPS 2025 · similarity 0.89)
- On Inference Stability for Diffusion Models (AAAI 2024 · similarity 0.89)
- O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions (ICLR 2025 · similarity 0.89)
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