Triangular-Reference Schr\"odinger Bridges for Time Series Generation

Researchers have proposed Generative SLiCEs, a continuous-time model for flow matching on path-space, and introduced Triangular-Reference Schrödinger Bridges for Time Series (TR-SBTS), an extension of the SBTS framework.

Generative SLiCEs, a maximally expressive model, improve performance in probabilistic forecasting and downstream tasks, according to a paper submitted to arXiv on May 27, 2026^[1]. The model is based on Structured Linear Controlled Differential Equations (SLiCEs), which are universal time-series generators. SLiCEs can approximate the induced path laws of continuous causal pushforwards on compact latent sets. TR-SBTS, introduced in a separate paper on arXiv^[2], replaces the Brownian reference with an intervalwise frozen diffusion reference. This construction is a single entropy projection on the augmented state space, preserving the variational core of SBTS. The entropy minimiser is the h-transform of the reference, realised through a finite-dimensional conditioning map. Generative SLiCEs retain the advantages of continuous-time models, such as generalising to arbitrary observation grids, which is beneficial for irregular grids where fixed-grid models often struggle^[1].