Universal time series generation with neural controlled differential equations

Preprint

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.

Authors: Berndt, T; Farjallah, E; Seute, L; Saqur, R; Walker, B

• Publication status: Published
• Preprint server: arXiv
• Publication date: 2026-05-27
• DOI: 10.48550/arXiv.2605.28507
• Server owner: Cornell University
• Language: English