Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on forecasting performance remains under-explored. In this work, we demonstrate that forecasting spatio-temporal data with flow matching is highly sensitive to the selection of the probability path model. Motivated by this insight, we propose a novel probability path model designed to improve forecasting performance. Our empirical results across various dynamical system benchmarks show that our model achieves faster convergence during training and improved predictive performance compared to existing probability path models. Importantly, our approach is efficient during inference, requiring only a few sampling steps. This makes our proposed model practical for real-world applications and opens new avenues for probabilistic forecasting.
Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 39 of its 57 references that are in the map. First posted on arXiv 4 Oct 2024.
Builds on
39 of 57 references.
Closest ancestors · 14
Same direction, newest first
- 2024Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling20 Aug
- 2024Discrete Flow Matching22 Jul
- 2024The Rise of Diffusion Models in Time-Series Forecasting5 Jan
- 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation4 Sep
- 2023Flow Matching in Latent Space17 Jul
- 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun
- 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplings28 Apr
- 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb
- 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models31 Jan
- 2022Efficient Video Prediction via Sparsely Conditioned Flow Matching26 Nov
- 2022Flow Matching for Generative Modeling6 Oct
- 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep
2 more
Other references · 25
- 2020Denoising Diffusion Probabilistic Modelscited by 20,851
- 2020Denoising Diffusion Implicit Modelscited by 9,655
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
- 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,094
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
- 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,526
- 2022Video Diffusion Modelscited by 2,280
- 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,725
- 2015Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcastingcited by 1,428
- 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
13 more
- 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
- 2021Score-based Generative Modeling in Latent Spacecited by 634
- 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
- 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
- 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
- 2023Photorealistic Video Generation with Diffusion Modelscited by 304
- 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 230
- 2020Forecasting Sequential Data using Consistent Koopman Autoencoderscited by 114
- 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 61
- 2021ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Modelscited by 42
- 2022Learning continuous models for continuous physicscited by 28
- 2021Stateful ODE-Nets using Basis Function Expansionscited by 14
- 2024Learning Physics for Unveiling Hidden Earthquake Ground Motions via Conditional Generative Modelingcited by 7
Built on by
Citing papers per year: 2025: 6; 2026: 6.
12 papers.
- 2025FLEX: A Backbone for Diffusion-Based Modeling of Spatio-temporal Physical Systemscited by 8
- 2025OAT-FM: Optimal Acceleration Transport for Improved Flow Matchingcited by 7
- 2025A Deep State Space Model for Rainfall-Runoff Simulationscited by 3
- 2025On The Hidden Biases of Flow Matching Samplerscited by 2
- 2026Probabilistic Precipitation Nowcasting with Rectified Flow Transformerscited by 2
- 2025FlowCast-ODE: Continuous Hourly Weather Forecasting with Dynamic Flow Matching and ODE Solvercited by 1
- 2025Operator Flow Matching for Timeseries Forecastingcited by 1
- 2026Variational Optimality of F"ollmer Processes in Generative Diffusionscited by 1
- 2026Trajectory-Aware Flow Matching for Topology Optimisationcited by 1
- 2026Autoregressive One-Step Generative Modeling for Dynamical System Forecastingcited by 0
- 2026Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matchingcited by 0
- 2026Variational Streaming Flow: Probabilistic Forecasting in Physical Timecited by 0
- 2026Variational Streaming Flow: Probabilistic Forecasting in Physical Time1 Oct 2026
- 2026Trajectory-Aware Flow Matching for Topology Optimisation16 Jul 2026
- 2026Probabilistic Precipitation Nowcasting with Rectified Flow Transformers29 May 2026
- 2026Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching12 May 2026
- 2026Autoregressive One-Step Generative Modeling for Dynamical System Forecasting7 May 2026
- 2026Variational Optimality of F"ollmer Processes in Generative Diffusions11 Feb 2026
- 2025On The Hidden Biases of Flow Matching Samplers18 Dec 2025
- 2025Operator Flow Matching for Timeseries Forecasting16 Oct 2025
- 2025OAT-FM: Optimal Acceleration Transport for Improved Flow Matching29 Sep 2025
- 2025FlowCast-ODE: Continuous Hourly Weather Forecasting with Dynamic Flow Matching and ODE Solver18 Sep 2025
- 2025FLEX: A Backbone for Diffusion-Based Modeling of Spatio-temporal Physical Systems23 May 2025
- 2025A Deep State Space Model for Rainfall-Runoff Simulations24 Jan 2025
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- 2026MercerFlow: Flow Matching in a Kernel-Induced Latent Space for Probabilistic Forecasting
- 2025Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching
- 2026Is Flow Matching Just Trajectory Replay for Sequential Data?
- 2024ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations
- 2026Probabilistic Geodesic Flow Matching on Location-Scale Families
- 2025TimeFlow: Towards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modeling