Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting

TL;DR

This paper introduces TSFlow, a novel probabilistic time series forecasting model that combines Gaussian processes with flow matching, improving generative quality and flexibility over traditional diffusion-based models.

Contribution

TSFlow integrates Gaussian processes into flow matching for better prior alignment, enabling improved probabilistic forecasting and data-dependent prior distributions.

Findings

High-quality unconditional samples produced

Competitive forecasting performance on benchmarks

Enhanced prior-data alignment improves generative modeling

Abstract

Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based models on a simple, fixed prior complicates the generative process since the data and prior distributions differ significantly. We introduce TSFlow, a conditional flow matching (CFM) model for time series combining Gaussian processes, optimal transport paths, and data-dependent prior distributions. By incorporating (conditional) Gaussian processes, TSFlow aligns the prior distribution more closely with the temporal structure of the data, enhancing both unconditional and conditional generation. Furthermore, we propose conditional prior sampling to enable probabilistic forecasting with an unconditionally trained model. In our experimental evaluation on eight real-world datasets, we demonstrate the generative capabilities of TSFlow, producing high-quality unconditional samples. Finally, we show that both conditionally and unconditionally trained models achieve competitive results across multiple forecasting benchmarks.