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.
Cite
@article{arxiv.2605.28507,
title = {Universal Time Series Generation with Neural Controlled Differential Equations},
author = {Torben Berndt and Elyes Farjallah and Leif Seute and Raeid Saqur and Benjamin Walker and Jan Stühmer},
journal= {arXiv preprint arXiv:2605.28507},
year = {2026}
}