SpectFlow: Long-term forecasting using flow matching with 89k parameters

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 SpectFlow, 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, SpectFlow 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 datasets demonstrate that SpectFlow achieves state-of-the-art forecasting performance, on average 7\%, while being significantly faster and more parameter-efficient than existing methods. This work bridges the generative power of continuous-time flows with the structural priors of spatio-temporal data, offering a practical and scalable solution for real-world forecasting applications.