# Series-to-Series Diffusion Bridge Model

arXiv: https://arxiv.org/abs/2411.04491 · HTML: https://mlsanity.com/paper/2411.04491/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [DINOISER: Diffused Conditional Sequence Learning by Manipulating Noises](https://mlsanity.com/paper/2302.10025/) (2023)
- [Image Restoration Through Generalized Ornstein-Uhlenbeck Bridge](https://mlsanity.com/paper/2312.10299/) (2023)
- [An Analysis of Linear Time Series Forecasting Models](https://mlsanity.com/paper/2403.14587/) (2024)
- [MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process](https://mlsanity.com/paper/2403.05751/) (2024)
- [Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis](https://mlsanity.com/paper/2312.03491/) (2023)
- [TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generation](https://mlsanity.com/paper/2408.06672/) (2024)

## Built on by (most cited first, 3 of 3)

- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion](https://mlsanity.com/paper/2505.11306/) (2025)
- [Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.20928/) (2025)

## Abstract (arXiv)

Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability arising from their inherent stochasticity. In this paper, we revisit time series diffusion models and present a comprehensive framework that encompasses most existing diffusion-based methods. Building on this theoretical foundation, we propose a novel diffusion-based time series forecasting model, the Series-to-Series Diffusion Bridge Model (S2DBM), which leverages the Brownian Bridge process to reduce randomness in reverse estimations and improves accuracy by incorporating informative priors and conditions derived from historical time series data. Experimental results demonstrate that S2DBM delivers superior performance in point-to-point forecasting and competes effectively with other diffusion-based models in probabilistic forecasting.