# Neural Stochastic Processes for Satellite Precipitation Refinement

arXiv: https://arxiv.org/abs/2604.10414 · HTML: https://mlsanity.com/paper/2604.10414/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 64 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Builds on (most cited first, 29 of 29)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Stochastic Super-Resolution for Downscaling Time-Evolving Atmospheric Fields with a Generative Adversarial Network](https://mlsanity.com/paper/2005.10374/) (2020)
- [ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction](https://mlsanity.com/paper/2402.00712/) (2024)
- [Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data](https://mlsanity.com/paper/2402.14989/) (2024)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [Convolutional conditional neural processes for local climate downscaling](https://mlsanity.com/paper/2101.07950/) (2021)
- [Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2301.11308/) (2023)
- [SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations](https://mlsanity.com/paper/2502.02472/) (2025)
- [Precipitation Downscaling with Spatiotemporal Video Diffusion](https://mlsanity.com/paper/2312.06071/) (2023)
- [RainNet: A Large-Scale Imagery Dataset and Benchmark for Spatial Precipitation Downscaling](https://mlsanity.com/paper/2012.09700/) (2020)
- [Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Series](https://mlsanity.com/paper/2410.05602/) (2024)
- [Flow Matching Neural Processes](https://mlsanity.com/paper/2512.23853/) (2025)
- [RainShift: A Benchmark for Precipitation Downscaling Across Geographies](https://mlsanity.com/paper/2507.04930/) (2025)

## Built on by (most cited first, 2 of 2)

- [Physics-Guided Flow-Map Matching for Precipitation Nowcasting](https://mlsanity.com/paper/2609.37487/) (2026)
- [Scale-Recursive Rectified Flows for Few-Step Precipitation Ensembles](https://mlsanity.com/paper/2610.02611/) (2026)

## Abstract (arXiv)

Accurate precipitation estimation is critical for flood forecasting, water resource management, and disaster preparedness. Satellite products provide global hourly coverage but contain systematic biases; ground-based gauges are accurate at point locations but too sparse for direct gridded correction. Existing methods fuse these sources by interpolating gauge observations onto the satellite grid, but treat each time step independently and therefore discard temporal structure in precipitation fields. We propose Neural Stochastic Process (NSP), a model that pairs a Neural Process encoder conditioning on arbitrary sets of gauge observations with a latent Neural SDE on a 2D spatial representation. NSP is trained under a single variational objective with simulation-free cost. We also introduce QPEBench, a benchmark of 43{,}756 hourly samples over the Contiguous United States (2021--2025) with four aligned data sources and six evaluation metrics. On QPEBench, NSP outperforms 13 baselines across all six metrics and surpasses JAXA's operational gauge-calibrated product. An additional experiment on Kyushu, Japan confirms generalization to a different region with independent data sources.