Mixture Reference Assisted Diffusion for Probabilistic Time Series Forecasting

Probabilistic time series forecasting is essential for simulating future states and supporting decision making. However, real world time series often exhibit temporal heterogeneity, where local statistical patterns shift across time. While diffusion models provide a flexible framework for capturing predictive uncertainty, conventional formulations rely on neural networks to learn these varying local patterns implicitly, complicating the reverse denoising process. To address this limitation, we introduce Mixture Reference Assisted Diffusion (MiraDiff), a framework that decouples conditional denoising into an analytical local statistical reference and a learnable neural correction. Specifically, MiraDiff first fits a Gaussian mixture to training segments to capture recurring local patterns. This frozen reference supplies closed form clean signal estimates across diffusion timesteps, while a neural network conditioned on observed history learns residual corrections to capture long range contexts and cross variable dependencies. Extensive experiments across eight real world datasets demonstrate that MiraDiff delivers consistently competitive probabilistic forecasting performance on both distribution calibration and temporal dependency fidelity. Further ablation studies confirm that introducing closed form local statistics provides an effective statistical inductive bias, substantially alleviating the learning burden on the neural network.