# Scale-Recursive Rectified Flows for Few-Step Precipitation Ensembles

arXiv: https://arxiv.org/abs/2610.02611 · HTML: https://mlsanity.com/paper/2610.02611/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## 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, 15 of 15)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models](https://mlsanity.com/paper/2310.13102/) (2023)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Wavelet Score-Based Generative Modeling](https://mlsanity.com/paper/2208.05003/) (2022)
- [Scale-Adaptive Generative Flows for Multiscale Scientific Data](https://mlsanity.com/paper/2509.02971/) (2025)
- [Efficient Kilometer-Scale Precipitation Downscaling with Conditional Wavelet Diffusion](https://mlsanity.com/paper/2507.01354/) (2025)
- [Multi-scale Generative Modeling for Fast Sampling](https://mlsanity.com/paper/2411.09356/) (2024)
- [Neural Stochastic Processes for Satellite Precipitation Refinement](https://mlsanity.com/paper/2604.10414/) (2026)
- [Colored Noise Diffusion Sampling](https://mlsanity.com/paper/2605.30332/) (2026)

## Abstract (arXiv)

Fine-resolution precipitation estimates support flood risk assessment and water management, but coarse satellite products cannot resolve rainfall within each grid cell. Generative models address this ambiguity by producing ensembles of plausible high-resolution rainfall fields. Among these models, rectified flows generate samples by iteratively transforming random noise into rainfall fields. Reducing the number of sampling steps accelerates generation but can make ensemble members too similar, understating uncertainty. We propose a scale-recursive rectified flow that generates broad patterns before local details and guides sampling-step allocation by comparing ensemble variability with prediction error across spatial scales. Validation scores and rainfall power spectra constrain the allocation to avoid excessive amplification. In satellite-to-radar downscaling over the contiguous United States, our analysis identified broad rainfall patterns as the main source of insufficient ensemble variability under reduced sampling budgets. Allocating more steps to the coarse flow improved probabilistic accuracy and rain detection across training seeds at fixed architecture and computational cost. The proposed model also achieved better probabilistic accuracy with shorter sampling time than a nonrecursive flow using more steps.