FreqFlow: Long-term forecasting using lightweight flow matching

TL;DR

FreqFlow introduces a lightweight, frequency-domain flow matching framework for deterministic multivariate time-series forecasting, achieving state-of-the-art accuracy with significantly fewer parameters and faster inference.

Contribution

It is the first to apply conditional flow matching in the spectral domain for efficient, long-term multivariate time-series forecasting.

Findings

Achieves 7% RMSE improvement over existing methods

Uses only 89k parameters, much fewer than diffusion models

Demonstrates faster inference and high accuracy on real-world datasets

Abstract

Multivariate time-series (MTS) forecasting is fundamental to applications ranging from urban mobility and resource management to climate modeling. While recent generative models based on denoising diffusion have advanced state-of-the-art performance in capturing complex data distributions, they suffer from significant computational overhead due to iterative stochastic sampling procedures that limit real-time deployment. Moreover, these models can be brittle when handling high-dimensional, non-stationary, and multi-scale periodic patterns characteristic of real-world sensor networks. We introduce FreqFlow, a novel framework that leverages conditional flow matching in the frequency domain for deterministic MTS forecasting. Unlike conventional approaches that operate in the time domain, FreqFlow transforms the forecasting problem into the spectral domain, where it learns to model amplitude and phase shifts through a single complex-valued linear layer. This frequency-domain formulation enables the model to efficiently capture temporal dynamics via complex multiplication, corresponding to scaling and temporal translations. The resulting architecture is exceptionally lightweight with only 89k parameters - an order of magnitude smaller than competing diffusion-based models-while enabling single-pass deterministic sampling through ordinary differential equation (ODE) integration. Our approach decomposes MTS signals into trend, seasonal, and residual components, with the flow matching mechanism specifically designed for residual learning to enhance long-term forecasting accuracy. Extensive experiments on real-world traffic speed, volume, and flow datasets demonstrate that FreqFlow achieves state-of-the-art forecasting performance, on average 7\% RMSE improvements, while being significantly faster and more parameter-efficient than existing methods