mlsanityData to 7 Oct 2026

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

arXiv 2607.21200 ↗First posted 23 Jul 2026stat.ML cs.LGcited by 0

On the map: Diffusion models → Flow matching, time series and science

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.

Key facts. No citing papers in the map yet (data through 7 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.

Builds on

38 of 72 references.

Closest ancestors · 5

Same direction, newest first

  1. 2026Elucidating the Design Space of Flow Matching for Cellular Microscopy25 Mar
  2. 2024Precipitation Nowcasting Using Diffusion Transformer with Causal Attention17 Oct
  3. 2024Diffusion-TS: Interpretable Diffusion for General Time Series Generation4 Mar
  4. 2023DDMT: Denoising Diffusion Mask Transformer Models for Multivariate Time Series Anomaly Detection13 Oct
  5. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul

Other references · 33

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  8. 2022Scalable Diffusion Models with Transformerscited by 5,931
  9. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,466
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  11. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  12. 2022DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generationcited by 3,286
21 more
  1. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  2. 2014Conditional Generative Adversarial Netscited by 2,152
  3. 2019Root Mean Square Layer Normalizationcited by 1,425
  4. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
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  6. 2021Vector Quantized Diffusion Model for Text-to-Image Synthesiscited by 773
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  21. 2023A stable deep adversarial learning approach for geological facies generationcited by 2

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