Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting

TL;DR

This paper investigates how the choice of probability path models in flow matching affects probabilistic time series forecasting, proposing a new model that enhances performance and efficiency.

Contribution

The paper introduces a novel probability path model for flow matching that improves forecasting accuracy and training convergence, with practical efficiency during inference.

Findings

Faster convergence during training.

Improved predictive performance.

Efficient inference with few sampling steps.

Abstract

Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on forecasting performance remains under-explored. In this work, we demonstrate that forecasting spatio-temporal data with flow matching is highly sensitive to the selection of the probability path model. Motivated by this insight, we propose a novel probability path model designed to improve forecasting performance. Our empirical results across various dynamical system benchmarks show that our model achieves faster convergence during training and improved predictive performance compared to existing probability path models. Importantly, our approach is efficient during inference, requiring only a few sampling steps. This makes our proposed model practical for real-world applications and opens new avenues for probabilistic forecasting.