FreqFlow: Long-term forecasting using lightweight flow matching

2025-11-20

AI Summary

Addressing the challenges of high computational cost, strong non-stationarity, and difficulty in modeling multi-scale periodic patterns in multivariate time series (MTS) long-term forecasting, this paper introduces conditional flow matching into frequency-domain modeling for the first time, proposing a lightweight deterministic forecasting framework. Methodologically, it employs frequency-domain transformation to decouple trend, seasonal, and residual components; designs a complex-valued linear layer to jointly model amplitude and phase dynamics; and leverages ODE integration for single-step deterministic sampling. The model contains only 89K parameters—approximately one order of magnitude fewer than mainstream diffusion-based approaches. On real-world traffic datasets, it achieves an average 7% reduction in RMSE and significantly accelerates inference. This work pioneers frequency-domain flow matching, achieving unprecedented balance among prediction accuracy, computational efficiency, and model compactness.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Planning with Language Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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

Problem

• Addresses computational inefficiency in diffusion models for time-series forecasting
• Handles high-dimensional non-stationary data with multi-scale periodic patterns
• Improves long-term forecasting accuracy through frequency-domain residual learning

Innovation

• Uses frequency-domain conditional flow matching
• Employs single complex-valued linear layer
• Decomposes signals into trend seasonal residual components