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Universal Time Series Generation with Neural Controlled Differential Equations

arXiv 2605.28507 ↗First posted 27 May 2026cs.LGcited by 0

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Abstract (arXiv)

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in W_∞. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 46 of its 65 references that are in the map. First posted on arXiv 27 May 2026.

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46 of 65 references.

References · 46

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
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34 more
  1. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
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  25. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 40
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  27. 2023State-space Models with Layer-wise Nonlinearity are Universal Approximators with Exponential Decaying Memorycited by 38
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  29. 2023Universality of Linear Recurrences Followed by Non-linear Projections: Finite-Width Guarantees and Benefits of Complex Eigenvaluescited by 35
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  34. 2025Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learningcited by 3

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  3. 2026Unconditional flow-based time series generation with equivariance-regularised latent spaces
  4. 2025Theoretical Foundation of Flow-Based Time Series Generation: Provable Approximation, Generalization, and Efficiency
  5. 2025Towards Stable and Structured Time Series Generation with Perturbation-Aware Flow Matching
  6. 2025TimeFlow: Towards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modeling
  7. 2023Effectively Modeling Time Series with Simple Discrete State Spaces
  8. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models