# Robust time series generation via Schr"odinger Bridge: a comprehensive evaluation

arXiv: https://arxiv.org/abs/2503.02943 · HTML: https://mlsanity.com/paper/2503.02943/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Deep Generative Learning via Schr"odinger Bridge](https://mlsanity.com/paper/2106.10410/) (2021)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial](https://mlsanity.com/paper/2402.07487/) (2024)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [Regular Time-series Generation using SGM](https://mlsanity.com/paper/2301.08518/) (2023)
- [Generative modeling for time series via Schr"odinger bridge](https://mlsanity.com/paper/2304.05093/) (2023)
- [High Rank Path Development: an approach of learning the filtration of stochastic processes](https://mlsanity.com/paper/2405.14913/) (2024)

## Built on by (most cited first, 8 of 8)

- [LightSBB-M: Bridging Schr"odinger and Bass for Generative Diffusion Modeling](https://mlsanity.com/paper/2601.19312/) (2026)
- [Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysis](https://mlsanity.com/paper/2510.11829/) (2025)
- [SBBTS: A Unified Schr"odinger-Bass Framework for Synthetic Financial Time Series](https://mlsanity.com/paper/2604.07159/) (2026)
- [ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space](https://mlsanity.com/paper/2604.27443/) (2026)
- [Diffusion Models for Adaptive Sequential Data Generation](https://mlsanity.com/paper/2606.06007/) (2026)
- [Markov Decision Processes of the Third Kind: Learning Distributions by Policy Gradient Descent](https://mlsanity.com/paper/2602.06567/) (2026)
- [Direct Estimation of Schr"odinger Bridge Time-Series Drifts: Finite-Sample, Asymptotic, and Adaptive Guarantees](https://mlsanity.com/paper/2605.05432/) (2026)
- [Deep-MKV-TS: Path-Dependent McKean--Vlasov Control for Financial Time Series Generation](https://mlsanity.com/paper/2608.19394/) (2026)

## Abstract (arXiv)

We investigate the generative capabilities of the Schr"odinger Bridge (SB) approach for time series. The SB framework formulates time series synthesis as an entropic optimal interpolation transport problem between a reference probability measure on path space and a target joint distribution. This results in a stochastic differential equation over a finite horizon that accurately captures the temporal dynamics of the target time series. While the SB approach has been largely explored in fields like image generation, there is a scarcity of studies for its application to time series. In this work, we bridge this gap by conducting a comprehensive evaluation of the SB method's robustness and generative performance. We benchmark it against state-of-the-art (SOTA) time series generation methods across diverse datasets, assessing its strengths, limitations, and capacity to model complex temporal dependencies. Our results offer valuable insights into the SB framework's potential as a versatile and robust tool for time series generation.