Universal Time Series Generation with Neural Controlled Differential Equations

• URL: http://arxiv.org/abs/2605.28507v1
• Date: Wed, 27 May 2026 14:10:41 GMT
• Title: Universal Time Series Generation with Neural Controlled Differential Equations
• Abstract summary: Generative SLiCEs is a maximally expressive continuous-time model for flow matching on path-space.<n>We show that expressivity improves performance in probabilistic forecasting and downstream tasks.<n>This is particularly beneficial for irregular grids, where fixed-grid models often struggle.
• Score: 4.084397270956687
• License: http://creativecommons.org/licenses/by/4.0/
• 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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