Series-to-Series Diffusion Bridge Model

Abstract

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 ($\mathrm{S^2DBM}$), 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 $\mathrm{S^2DBM}$ delivers superior performance in point-to-point forecasting and competes effectively with other diffusion-based models in probabilistic forecasting.