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Universal Time Series Generation with Neural Controlled Differential Equations

NeurIPS 2026 · Time series › Causal and generative time series · approach: Neural differential equations · 0 citations (OpenAlex)

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Proves that maximally expressive Structured Linear CDEs are universal causal time-series generators in W_infinity, and introduces G-SLiCE, a path-space flow-matching model that achieves competitive CRPS and better robustness to sampling-grid shifts than TSFlow.

Problem

Generative probabilistic time-series forecasting and generation uses sequence backbones (e.g., S4 in TSFlow) that are not maximally expressive, and fixed-grid discrete models struggle under changes in observation grid, including irregular sampling.

Approach

Proves pathwise universality of SLiCEs implies distributional (W_infinity) universality of their pushforward path laws, then uses a SLiCE backbone as the vector field in conditional flow matching on path space (G-SLiCE), with GP priors, so the model is evaluated in continuous time.

Key results

• G-SLiCEs achieves the best CRPS on 6 of 8 GluonTS datasets in probabilistic forecasting and beats TSFlow on 7 of 8 (e.g., Electricity 0.044 vs 0.045, M4-H 0.023 vs 0.028).
• On ETTSmall 15min-train/12h-test cross-frequency generalisation, G-SLiCE attains CRPS 0.189 while direct TSFlow reaches 906.205.
• On irregular grids with k_train=100, TSFlow has CRPS 0.21 and NRMSE 1.72 versus G-SLiCE CRPS 0.13 and NRMSE 0.27.

Surprising findings

• The authors could not reproduce the reported TSFlow result on Wiki2000; their best reproduced CRPS was 0.218 versus 0.207 reported.
• Dense transition blocks are not selected on all datasets, suggesting extra expressivity is only sometimes needed.

Limitations

• Current implementation uses a first-order approximation of the matrix exponential; efficient GPU kernels for structured matrix exponentials remain open.
• Theory does not fully characterise which path-space distributional maps are reachable by ODE-based flow-matching training.
• Non-compact Gaussian process priors only yield high-probability rather than exact W_infinity guarantees.

Experimental setup

Datasets: Electricity Exchange KDDCup M4-Hourly Solar Traffic UberTLC-Hourly Wikipedia ETTSmall

Benchmarks: Electricity Exchange KDDCup M4-Hourly Solar Traffic UberTLC-Hourly Wiki2000 ETTSmall

Metrics: CRPS 2-Wasserstein distance Linear Predictive Score NRMSE

Baselines: TSFlow CSDI SSSD TSDiff DeepAR TFT WaveNet PatchTST DLinear AutoARIMA AutoETS Seasonal Naive

Builds on: TSFlow conditional flow matching Neural CDE S4 Mamba

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