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DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting

NeurIPS 2026 · Time series › Causal and generative time series · approach: Diffusion models for time series · 0 citations (OpenAlex)

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Rethinks the diffusion ELBO under a location-scale noise model for probabilistic time series forecasting and proposes DiffPTS, which jointly trains mean/variance estimators and the denoiser via the full ELBO.

Problem

Diffusion-based probabilistic time series forecasting methods add pretrained mean and variance estimators to the diffusion process, but train them with ad-hoc regression targets outside the variational (ELBO) framework, leaving reconstruction and prior-matching terms unoptimized.

Approach

Under the location-scale noise model, the full ELBO (reconstruction, prior matching, denoising) induces a Gaussian negative log-likelihood objective for the mean and variance estimators, so they can be trained end-to-end jointly with the denoiser; the ELBO also unifies residual-based and endpoint-based diffusion forecasters (NsDiff, RDIT, D3U, TMDM, DDPM).

Key results

• On ECL, DiffPTS reduces CRPS by 24.8% (0.290 to 0.218) and MSE by 13.9% (0.209 to 0.180) relative to NsDiff.
• On Traffic, DiffPTS reduces CRPS from 0.378 to 0.270 and MSE from 0.637 to 0.456 relative to NsDiff.
• Plug-in DiffPTS improves NsDiff, RDIT and D3U on all four ETT datasets; D3U+DiffPTS on ETTm1 reduces CRPS from 0.412 to 0.290 and MSE from 0.589 to 0.357.

Surprising findings

• The prior-matching and reconstruction terms, usually treated as constants in DDPM, are non-negligible once adaptive estimators are introduced.
• Even the variant trained only on the NLL objective (w/o denoise) remains competitive with the full model on several datasets.

Limitations

• Focuses on the optimization objective and does not study architecture choices for the estimators or the denoiser.
• Does not address faster inference; sampling requires many reverse steps.
• The uncertainty-aware NsDiff noise schedule is not combined with the label-free objective.

Experimental setup

Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity (ECL) Influenza-like Illness (ILI) Exchange Rate (EXR) Traffic Solar Energy

Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 ECL ILI EXR Traffic Solar

Metrics: CRPS MSE

Baselines: TimeGrad CSDI TimeDiff TMDM DiffusionTS D3U RDIT NsDiff

Builds on: DDPM NsDiff RDIT D3U TMDM

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