# HydroDiffusion: Diffusion-Based Probabilistic Streamflow Forecasting with a State Space Backbone

arXiv: https://arxiv.org/abs/2512.12183 · HTML: https://mlsanity.com/paper/2512.12183/

## Key facts

- Cited by 2 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 23 of its 65 references that are in the map.
- First posted on arXiv 13 Dec 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, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [FuXi-Extreme: Improving extreme rainfall and wind forecasts with diffusion model](https://mlsanity.com/paper/2310.19822/) (2023)
- [MC-LSTM: Mass-Conserving LSTM](https://mlsanity.com/paper/2101.05186/) (2021)
- [Tuning Frequency Bias of State Space Models](https://mlsanity.com/paper/2410.02035/) (2024)
- [Probing the limit of hydrologic predictability with the Transformer network](https://mlsanity.com/paper/2306.12384/) (2023)
- [FLEX: A Backbone for Diffusion-Based Modeling of Spatio-temporal Physical Systems](https://mlsanity.com/paper/2505.17351/) (2025)
- [Time Series Predictions in Unmonitored Sites: A Survey of Machine Learning Techniques in Water Resources](https://mlsanity.com/paper/2308.09766/) (2023)
- [A Deep State Space Model for Rainfall-Runoff Simulations](https://mlsanity.com/paper/2501.14980/) (2025)
- [Improving ensemble extreme precipitation forecasts using generative artificial intelligence](https://mlsanity.com/paper/2407.04882/) (2024)
- [Towards CONUS-Wide ML-Augmented Conceptually-Interpretable Modeling of Catchment-Scale Precipitation-Storage-Runoff Dynamics](https://mlsanity.com/paper/2510.02605/) (2025)

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

- [AIFL: A Global Daily Streamflow Forecasting Model Using a Deterministic LSTM Pre-trained on ERA5-Land and Fine-tuned on IFS](https://mlsanity.com/paper/2602.16579/) (2026)
- [Distributed Hydrological Modeling in the Feature Space](https://mlsanity.com/paper/2609.32971/) (2026)

## Abstract (arXiv)

Recent advances have introduced diffusion models for probabilistic streamflow forecasting, demonstrating strong early flood-warning skill. However, current implementations rely on recurrent Long Short-Term Memory (LSTM) backbones and single-step training objectives, which limit their ability to capture long-range dependencies and produce coherent forecast trajectories across lead times. To address these limitations, we developed HydroDiffusion, a diffusion-based probabilistic forecasting framework with a decoder-only state space model backbone. The proposed framework jointly denoises full multi-day trajectories in a single pass, ensuring temporal coherence and mitigating error accumulation common in autoregressive prediction. HydroDiffusion is evaluated across 531 watersheds in the contiguous United States (CONUS) in the CAMELS dataset. We benchmark HydroDiffusion against two diffusion baselines with LSTM backbones, as well as the recently proposed Diffusion-based Runoff Model (DRUM). Results show that HydroDiffusion achieves strong nowcast accuracy when driven by observed meteorological forcings, and maintains consistent performance across the full simulation horizon. Moreover, HydroDiffusion delivers stronger deterministic and probabilistic forecast skill than DRUM in operational forecasting. These results establish HydroDiffusion as a robust generative modeling framework for medium-range streamflow forecasting, providing both a new modeling benchmark and a foundation for future research on probabilistic hydrologic prediction at continental scales.