MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process

TL;DR

MG-TSD tackles probabilistic time-series forecasting with diffusion models by exploiting intrinsic multi-granularity structure in data as intermediate guidance. It derives a multi-granularity guidance diffusion loss and implements a training scheme where coarse-grained targets guide intermediate diffusion steps, using a shared denoiser and variance schedule across granularities. Experiments on six real-world datasets show state-of-the-art performance across CRPS_sum, NMAE_sum, and NRMSE_sum, with robust long-horizon forecasting. The approach does not require external data, enhancing applicability while stabilizing sampling and improving forecast fidelity. Overall, the work highlights multi-granularity signals as a powerful supervision mechanism for diffusion-based probabilistic forecasting.

Abstract

Recently, diffusion probabilistic models have attracted attention in generative time series forecasting due to their remarkable capacity to generate high-fidelity samples. However, the effective utilization of their strong modeling ability in the probabilistic time series forecasting task remains an open question, partially due to the challenge of instability arising from their stochastic nature. To address this challenge, we introduce a novel Multi-Granularity Time Series Diffusion (MG-TSD) model, which achieves state-of-the-art predictive performance by leveraging the inherent granularity levels within the data as given targets at intermediate diffusion steps to guide the learning process of diffusion models. The way to construct the targets is motivated by the observation that the forward process of the diffusion model, which sequentially corrupts the data distribution to a standard normal distribution, intuitively aligns with the process of smoothing fine-grained data into a coarse-grained representation, both of which result in a gradual loss of fine distribution features. In the study, we derive a novel multi-granularity guidance diffusion loss function and propose a concise implementation method to effectively utilize coarse-grained data across various granularity levels. More importantly, our approach does not rely on additional external data, making it versatile and applicable across various domains. Extensive experiments conducted on real-world datasets demonstrate that our MG-TSD model outperforms existing time series prediction methods.

Figures (8)

• Figure 1: The process of smoothing data from finest-grained to coarsest-grained naturally aligns with the diffusion process.
• Figure 2: Overview of the Multi-Granularity Time Series Diffusion (MG-TSD) model, consisting of three key modules: Multi-granularity Data Generator, Temporal Process Module (TPM), and Guided Diffusion Process Module for time series forecasting at a specific granularity level.
• Figure 3: Selection of share ratio for MG-TSD models
• Figure 4: Visualization of the ground-truth (Solar dataset), MG-TSD predicted mean for 4-hour and 1-hour time series, and TimeGrad predicted mean for the 1-hour time series. Additionally, the 50% prediction intervals for the 1-hour data are also included. These plots represent some illustrative dimensions out of 370 dimensions from the first 24-hour rolling-window.
• Figure 5: Performance evaluation across different prediction horizons for MG-TSD with TimeGrad as the baseline Model. The context length is fixed at 24h and the prediction length is tested at 24h, 48h, 96h, and 144h. The average CRPS, NRMSE, and NMAE metrics are computed for both MG-TSD and the baseline over 10 independent runs, with error bars indicating the corresponding standard deviations.