Problem
Research questions and friction points this paper is trying to address.
time series generation
universal approximation
continuous-time models
irregular grids
path-space generative modeling
Universal Time Series Generation with Neural Controlled Differential Equations
🤖 AI Summary
Existing time series generative models suffer from limited expressivity and poor adaptability to irregularly sampled observation grids. This work proposes G-SLiCEs, a continuous-time generative model based on Structured Linear Controlled differential equations (SLiCEs), which achieves high expressivity through continuous flow matching in path space. We establish, for the first time, that SLiCEs can approximate any continuous causal pushforward path law under the Wasserstein-∞ metric, thereby enabling universal time series generation and introducing maximal expressivity into continuous-time generative modeling. The method natively supports arbitrary observation time grids and significantly outperforms existing approaches in irregularly sampled settings, demonstrating superior performance in probabilistic forecasting and downstream tasks.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Neural Controlled Differential Equations
Universal Time Series Generation
Structured Linear CDEs
Continuous-time Generative Modeling
Path-space Flow Matching
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