Probabilistic Forecasting via Autoregressive Flow Matching

Ahmed ElGazzar, Marcel van Gerven

Keywords: Forecasting, Dynamical systems, Generative Modeling, Flow Matching

TL;DR: We propose a method for sample-effcient forecasting of multivariate timeseries data via autoregressive flow matching.

Abstract:

In this work, we introduce autoregressive flow matching (AFM) for probabilistic forecasting of multivariate timeseries data. Given historical measurements and optional future covariates, we formulate forecasting as sampling from a learned conditional distribution over future trajectories. Specifically, we decompose the joint distribution of future observations into a sequence of conditional densities, each modeled via a shared flow that transforms a simple base distribution into the next observation distribution, conditioned on observed covariates. To achieve this, we leverage the flow matching framework, enabling scalable and simulation-free learning of these transformations.
By combining this factorization with the flow matching objective, AFM retains the benefits of classical autoregressive models—including strong extrapolation performance, compact model size, and well-calibrated uncertainty estimates—while also capturing complex multi-modal conditional distributions, as seen in modern transport-based generative models. We demonstrate the effectiveness of AFM on multiple stochastic dynamical systems and real-world forecasting tasks.

Primary Area: learning on time series and dynamical systems

Submission Number: 11371