Stochastic Diffusion: A Diffusion Based Model for Stochastic Time Series Forecasting

Recent successes in diffusion probabilistic models have demonstrated their strength in modeling and generating different types of data, paving the way for their application in generative time series forecasting.However, most existing diffusion based approaches rely on sequential models and unimodal latent variables to capture global dependencies and model entire observable data, resulting in difficulties when it comes to highly stochastic time series data.In this paper, we propose a novel Stochastic Diffusion (StochDiff) model that integrates the diffusion process into time series modeling stage and utilizes the representational power of the stochastic latent spaces to capture the variability of the stochastic time series data.Specifically, the model applies diffusion module at each time step within the sequential framework and learns a step-wise, datadriven prior for generative diffusion process.These features enable the model to effectively capture complex temporal dynamics and the multi-modal nature of the highly stochastic time series data.Through extensive experiments on real-world datasets, we demonstrate the effectiveness of our proposed model for probabilistic time series forecasting, particularly in scenarios with high stochasticity.Additionally, with a real-world surgical use case, we highlight the model's potential in a medical application.