# Transformer-based Diffusion models for Hydrological Time Series Probabilistic Imputation and Forecasting

arXiv: https://arxiv.org/abs/2607.21200 · HTML: https://mlsanity.com/paper/2607.21200/

## 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 38 of its 72 references that are in the map.
- First posted on arXiv 23 Jul 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, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [U2-Net: Going Deeper with Nested U-Structure for Salient Object Detection](https://mlsanity.com/paper/2005.09007/) (2020)
- [Diffsound: Discrete Diffusion Model for Text-to-sound Generation](https://mlsanity.com/paper/2207.09983/) (2022)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [cosFormer: Rethinking Softmax in Attention](https://mlsanity.com/paper/2202.08791/) (2022)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [Enhancing streamflow forecast and extracting insights using long-short term memory networks with data integration at continental scales](https://mlsanity.com/paper/1912.08949/) (2019)

## Abstract (arXiv)

The modeling of hydrometeorological time series with limited observations is a key challenge in the monitoring of hydro-systems and water resources, as well as for flood or drought risk assessment. Due to the high variability of the underlying processes and the sparsity of available measurements, traditional statistical approaches often struggle to accurately represent their dynamics. In this context, recent advances in deep learning offer a promising direction for improving the representation and generation of complex temporal processes sampled at several observation sites. This study investigates the application of transformer-based diffusion models to the simulation and reconstruction of hydrological time series. The proposed framework is applied to the joint modeling of water quantity and quality at six sites spread across three adjacent headwater catchments located in North-East France on a limestone plateau covered by forests and field crops. The model is calibrated and validated using available observational data, which has been quality controlled and corrected for sensor drift and malfunction through collaborative efforts by LNE metrology expertise and Andra monthly quality control over more than 15 years. Its performance is compared with several established baseline approaches commonly used for time series modeling. Quantitative evaluation metrics are employed to assess the ability of the proposed method to reproduce key temporal characteristics of the observed signals in two settings: the imputation of incomplete time series and the forecasting of upcoming hydrological conditions. Results support the effectiveness of the transformer-based approach and highlight its capacity to capture and simulate the complex patterns present in hydrological data. In particular, the results indicate that diffusion models can efficiently sample realistic time series distributions under observation settings with variable missing data for both forecasting and imputation.