# Probabilistic Forecasting via Autoregressive Flow Matching

arXiv: https://arxiv.org/abs/2503.10375 · HTML: https://mlsanity.com/paper/2503.10375/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [Time Series Analysis and Modeling to Forecast: a Survey](https://mlsanity.com/paper/2104.00164/) (2021)

## Built on by (most cited first, 9 of 9)

- [A Jump-Diffusion Framework for Irregular Time Series Generation](https://mlsanity.com/paper/2505.23215/) (2025)
- [Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems](https://mlsanity.com/paper/2511.04641/) (2025)
- [Probabilistic Prediction of Neural Dynamics via Autoregressive Flow Matching](https://mlsanity.com/paper/2604.11178/) (2026)
- [Autoregressive One-Step Generative Modeling for Dynamical System Forecasting](https://mlsanity.com/paper/2605.05540/) (2026)
- [(HB-ARFM) History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction](https://mlsanity.com/paper/2606.00349/) (2026)
- [Amortized Interventional Forecasting for Multivariate CIR Processes](https://mlsanity.com/paper/2608.03715/) (2026)
- [Time series generation with spectrally aligned latent flow matching](https://mlsanity.com/paper/2609.21989/) (2026)
- [Variational Streaming Flow: Probabilistic Forecasting in Physical Time](https://mlsanity.com/paper/2610.00976/) (2026)
- [ProtoFlow: Prototype-Guided Flow Matching for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2610.01320/) (2026)

## Abstract (arXiv)

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.