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arXiv · 2605.28507

Universal Time Series Generation with Neural Controlled Differential Equations

Torben Berndt·Elyes Farjallah·Leif Seute·Raeid Saqur·Benjamin Walker·Jan Stühmer
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Abstract

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 $W_\infty$. 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.

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Torben Berndt, Elyes Farjallah, Leif Seute, Raeid Saqur, Benjamin Walker, Jan Stühmer. 2026-06-11. Universal Time Series Generation with Neural Controlled Differential Equations. https://arxiv.org/abs/2605.28507

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