# Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2410.03024 · HTML: https://mlsanity.com/paper/2410.03024/

## Key facts

- Cited by 43 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 38 of its 49 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## 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, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [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)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [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)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [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)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Diffusion Self-Guidance for Controllable Image Generation](https://mlsanity.com/paper/2306.00986/) (2023)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [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)

## Built on by (most cited first, 30 of 43)

- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [Fast and Robust Visuomotor Riemannian Flow Matching Policy](https://mlsanity.com/paper/2412.10855/) (2024)
- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [Probabilistic Forecasting via Autoregressive Flow Matching](https://mlsanity.com/paper/2503.10375/) (2025)
- [Efficient Flow Matching using Latent Variables](https://mlsanity.com/paper/2505.04486/) (2025)
- [Byte Pair Encoding for Efficient Time Series Forecasting](https://mlsanity.com/paper/2505.14411/) (2025)
- [Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching](https://mlsanity.com/paper/2507.07192/) (2025)
- [Is There a Better Source Distribution than Gaussian? Exploring Source Distributions for Image Flow Matching](https://mlsanity.com/paper/2512.18184/) (2025)
- [Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matching](https://mlsanity.com/paper/2411.07625/) (2024)
- [Generative Modeling with Bayesian Sample Inference](https://mlsanity.com/paper/2502.07580/) (2025)
- [Is Flow Matching Just Trajectory Replay for Sequential Data?](https://mlsanity.com/paper/2602.08318/) (2026)
- [Spatiotemporal Imputation with Graph-Informed Flow Matching](https://mlsanity.com/paper/2606.06682/) (2026)
- [Towards Stable and Structured Time Series Generation with Perturbation-Aware Flow Matching](https://mlsanity.com/paper/2511.14488/) (2025)
- [Operator Flow Matching for Timeseries Forecasting](https://mlsanity.com/paper/2510.15101/) (2025)
- [LLM Flow Processes for Text-Conditioned Regression](https://mlsanity.com/paper/2601.06147/) (2026)
- [PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation](https://mlsanity.com/paper/2605.28867/) (2026)
- [Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.20928/) (2025)
- [Energy-Guided Generative Modeling for Low-Energy Molecular Structure Discovery](https://mlsanity.com/paper/2512.22597/) (2025)
- [Unconditional flow-based time series generation with equivariance-regularised latent spaces](https://mlsanity.com/paper/2601.22848/) (2026)
- [CoGenCast: A Coupled Autoregressive-Flow Generative Framework for Time Series Forecasting](https://mlsanity.com/paper/2602.03564/) (2026)
- [Native Extrapolation Awareness in Flow-Based Conditional Generation](https://mlsanity.com/paper/2602.13061/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Probabilistic Prediction of Neural Dynamics via Autoregressive Flow Matching](https://mlsanity.com/paper/2604.11178/) (2026)
- [Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics](https://mlsanity.com/paper/2604.17670/) (2026)
- [Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2605.23402/) (2026)
- [Universal Time Series Generation with Neural Controlled Differential Equations](https://mlsanity.com/paper/2605.28507/) (2026)
- [PAMF: Prior-Aware Multimodal Fusion for Incomplete Time Series Data](https://mlsanity.com/paper/2606.06328/) (2026)
- [B[FM]2: Brain Foundation Model via Flow Matching with SplitUNet](https://mlsanity.com/paper/2606.20812/) (2026)

## Abstract (arXiv)

Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based models on a simple, fixed prior complicates the generative process since the data and prior distributions differ significantly. We introduce TSFlow, a conditional flow matching (CFM) model for time series combining Gaussian processes, optimal transport paths, and data-dependent prior distributions. By incorporating (conditional) Gaussian processes, TSFlow aligns the prior distribution more closely with the temporal structure of the data, enhancing both unconditional and conditional generation. Furthermore, we propose conditional prior sampling to enable probabilistic forecasting with an unconditionally trained model. In our experimental evaluation on eight real-world datasets, we demonstrate the generative capabilities of TSFlow, producing high-quality unconditional samples. Finally, we show that both conditionally and unconditionally trained models achieve competitive results across multiple forecasting benchmarks.