Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Probabilistic Forecasting via Autoregressive Flow Matching

Ahmed El-Gazzar, Marcel van Gerven

TL;DR

FlowTime introduces autoregressive flow matching for probabilistic forecasting of multivariate time series by decomposing the future into a sequence of conditional distributions modeled with a shared flow. It leverages a conditional flow matching objective to train a velocity field that transports a simple base distribution toward the target conditional trajectory distribution, enabling efficient sampling via ODE integration. The autoregressive factorization improves extrapolation, uncertainty calibration, and scalability to high-dimensional data, and it shows strong performance on both stochastic dynamical systems and real-world forecasting tasks, often outperforming non-autoregressive FM and traditional baselines. The approach offers a practical, principled framework for accurate and calibrated probabilistic forecasts with potential for extensions to latent representations and irregular sampling in future work.

Abstract

In this work, we propose FlowTime, a generative model 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 (FM) framework, enabling scalable and simulation-free learning of these transformations. By combining this factorization with the FM objective, FlowTime retains the benefits of 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 FlowTime on multiple dynamical systems and real-world forecasting tasks.

Probabilistic Forecasting via Autoregressive Flow Matching

TL;DR

FlowTime introduces autoregressive flow matching for probabilistic forecasting of multivariate time series by decomposing the future into a sequence of conditional distributions modeled with a shared flow. It leverages a conditional flow matching objective to train a velocity field that transports a simple base distribution toward the target conditional trajectory distribution, enabling efficient sampling via ODE integration. The autoregressive factorization improves extrapolation, uncertainty calibration, and scalability to high-dimensional data, and it shows strong performance on both stochastic dynamical systems and real-world forecasting tasks, often outperforming non-autoregressive FM and traditional baselines. The approach offers a practical, principled framework for accurate and calibrated probabilistic forecasts with potential for extensions to latent representations and irregular sampling in future work.

Abstract

In this work, we propose FlowTime, a generative model 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 (FM) framework, enabling scalable and simulation-free learning of these transformations. By combining this factorization with the FM objective, FlowTime retains the benefits of 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 FlowTime on multiple dynamical systems and real-world forecasting tasks.

Paper Structure

This paper contains 32 sections, 19 equations, 2 figures, 4 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background: Flow matching
  3. Autoregressive Flow Matching
  4. Problem Setting
  5. Constructing a target probability path
  6. Training
  7. Inference
  8. Experiments
  9. Dynamical systems
  10. Data
  11. Implementation details
  12. Baselines
  13. Evaluation
  14. Results
  15. Real-world datasets
  16. ...and 17 more sections

Figures (2)

  • Figure 1: An overview of the training and sampling process of our approach. During training, a probability path $(p^s)^{0 \leq s \leq 1}$ is constructed between a base distribution $p^0$ and the target distribution $p^1$. This probability path is generated by a velocity field $\mu$. Training is done by regressing $\mu$ via a neural network $\nu_\theta$ which takes in a sample from the probability path $\mathbf{y}^s_t$ at flow step $s$, a context vector $\mathbf{h}_t$ encoding past observations and covariates, and the current covariate $\mathbf{c}_t$. After training, sampling from the target distribution is achieved via first sampling the base distribution $p^0$, and integrating the trained velocity field via a ODE solver until $s=1$.
  • Figure 2: Samples from the forecasting results for autoregressive flow matching vs standard flow matching on four different dynamical systems. The solid lines indicate ground truth, while the dashed lines indicated the mean prediction along with the 95$\%$ confidence interval. The results are visualized during both prediction and extrapolation regimes.