Learning Multimodal Predictive Regions with Diffusion: Conformal Prediction for Multivariate Time Series

Multivariate time series forecasting informs decision making in domains such as traffic and energy systems. In these domains, effective decisions require understanding the uncertainty in future outcomes and the dependencies between them. To quantify this uncertainty, conformal prediction offers a model-agnostic way to calibrate multivariate prediction regions. However, it typically assumes exchangeability, which is generally violated by temporally dependent data. In addition, conformal prediction relies on connected regions, which is inefficient for systems like traffic or energy models when the predictive distribution is multimodal or non-connected. We address both issues using a conditional diffusion model within a conformal framework. Rather than running the reverse diffusion process, we use denoising errors to assess how well a possible future outcome $y$ fits the learned conditional distribution. These errors are averaged into a scalar nonconformity score and calibrated using split conformal prediction. For finite samples from strictly stationary $\beta$-mixing time series, we establish bounds on marginal and conditional coverage, with a small penalty for temporal dependence. Experiments on non-Gaussian multimodal VAR processes and the Traffic and Solar datasets show competitive coverage/volume tradeoffs, with at least 7% smaller prediction regions in strongly multimodal settings.