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

TL;DR

StochDiff introduces a diffusion-based framework that integrates the diffusion process into time-series modeling at each step, guided by a data-driven prior ${\bm{z}}_t$ learned from the temporal context. By coupling an LSTM-based prior encoder with a cross-attentive diffusion module, the model captures multimodal and highly stochastic dynamics in multivariate sequences and uses a Gaussian Mixture Model to produce accurate point estimates. Across six real-world datasets, StochDiff achieves competitive results on homogeneous series and clear advantages on heterogeneous clinical data, including notable improvements in CRPS on ECochG and MMG. A real-world Cochlear Implant Surgery case study demonstrates practical applicability and real-time forecasting capability, while ablations and limitations point to opportunities for architectural refinement and ethical deployment. Overall, the method advances probabilistic time-series forecasting by tightly integrating data-driven priors with step-wise diffusion to model uncertainty and multi-modality in complex domains.

Abstract

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to model highly stochastic time series data remains a challenge. In this paper, we propose a novel Stochastic Diffusion (StochDiff) model which learns data-driven prior knowledge at each time step by utilizing the representational power of the stochastic latent spaces to model the variability of the multivariate time series data. The learnt prior knowledge helps the model to capture complex temporal dynamics and the inherent uncertainty of the data. This improves its ability to model highly stochastic time series data. Through extensive experiments on real-world datasets, we demonstrate the effectiveness of our proposed model on stochastic time series forecasting. Additionally, we showcase an application of our model for real-world surgical guidance, highlighting its potential to benefit the medical community.

Figures (7)

• Figure 1: Stochastic Diffusion for Time Series Forecasting
• Figure 2: Graphic illustration of the modeling operations of StochDiff. (1) Obtaining conditional prior. (2) Inference of approximate posterior. (3) Hidden state update via sequential model. (4) Data generation via diffusion model.
• Figure 3: Attention-Net
• Figure 4: Forecasting results of 4 the best models (based on quantitative results). We display the entire prediction range together with the $90\%$ prediction interval via green bars. The orange dashed lines represent the point-wise results which are medians for baseline methods and the largest centers of fitted GMM for our model.
• Figure 5: Cochlear Implant Forecasting Simulations. The blue line is the real CM amplitude, and the orange part is the observation that was fed to the model. Forecasting from different models are marked with differently according to the legend inside the plots.