# Generating ensembles of spatially-coherent in-situ forecasts using flow matching

arXiv: https://arxiv.org/abs/2504.03463 · HTML: https://mlsanity.com/paper/2504.03463/

## Key facts

- Cited by 3 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 21 of its 47 references that are in the map.
- First posted on arXiv 4 Apr 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, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Multistep Distillation of Diffusion Models via Moment Matching](https://mlsanity.com/paper/2406.04103/) (2024)
- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison](https://mlsanity.com/paper/2106.09512/) (2021)
- [ArchesWeather & ArchesWeatherGen: a deterministic and generative model for efficient ML weather forecasting](https://mlsanity.com/paper/2412.12971/) (2024)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling](https://mlsanity.com/paper/1302.7149/) (2013)
- [Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rules](https://mlsanity.com/paper/1910.07325/) (2019)

## Built on by (most cited first, 3 of 3)

- [Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training](https://mlsanity.com/paper/2605.13175/) (2026)
- [ProFlow: Zero-Shot Physics-Consistent Sampling via Proximal Flow Guidance](https://mlsanity.com/paper/2601.20227/) (2026)
- [STIPP: Space-time in situ postprocessing over the French Alps using proper scoring rules](https://mlsanity.com/paper/2601.02882/) (2026)

## Abstract (arXiv)

We propose a machine-learning-based methodology for in-situ weather forecast postprocessing that is both spatially coherent and multivariate. Compared to previous work, our Flow MAtching Postprocessing (FMAP) better represents the correlation structures of the observations distribution, while also improving marginal performance at the stations. FMAP generates forecasts that are not bound to what is already modeled by the underlying gridded prediction and can infer new correlation structures from data. The resulting model can generate an arbitrary number of forecasts from a limited number of numerical simulations, allowing for low-cost forecasting systems. A single training is sufficient to perform postprocessing at multiple lead times, in contrast with other methods which use multiple trained networks at generation time. This work details our methodology, including a spatial attention transformer backbone trained within a flow matching generative modeling framework. FMAP shows promising performance in experiments on the EUPPBench dataset, forecasting surface temperature and wind gust values at station locations in western Europe up to five-day lead times.