ChaosDiff: Jointly-Trained Diffusion Model

Chaos exists widely in meteorological, economic, and physical systems. However, its inherent characteristics, such as sensitivity to initial conditions, long-term nonstationarity, and complex nonlinear dynamics, severely limit the accuracy of chaotic data forecasting. Traditional diffusion models typically use independently trained modules and assume overly simplistic Gaussian distributions in latent variable spaces. These simplified assumptions are inadequate for capturing the intricate topological structures of chaotic attractors, leading to a significant drop in forecasting performance. To address this issue, this paper proposes a model named ChaosDiff, an end-to-end jointly-trained diffusion model framework. In this model, the conventional Gaussian assumption is removed, allowing the latent variable space to more accurately reflect the complex topological and dynamic features of chaotic time series. Experimental results on classical chaotic systems, including Lorenz, Rössler, and a piecewise-linear hyperchaotic system, show that ChaosDiff significantly outperforms existing methods in terms of forecasting accuracy and generalization ability.