# Diffusion Model-Based Data Assimilation for Real-World Energy Consumption Forecasting

arXiv: https://arxiv.org/abs/2605.29072 · HTML: https://mlsanity.com/paper/2605.29072/

## 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 9 of its 35 references that are in the map.
- First posted on arXiv 27 May 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, 9 of 9)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Ensemble score filter with image inpainting for data assimilation in tracking surface quasi-geostrophic dynamics with partial observations](https://mlsanity.com/paper/2501.12419/) (2025)
- [A Score-based Nonlinear Filter for Data Assimilation](https://mlsanity.com/paper/2306.09282/) (2023)
- [A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics](https://mlsanity.com/paper/2407.12168/) (2024)
- [An Online Algorithm for Solving Feedback Optimal Control Problems with Partial Observations](https://mlsanity.com/paper/2404.05734/) (2024)

## Abstract (arXiv)

Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management. In practice, however, complete and timely measurements may not always be available, and the observed data can be partial, noisy, or delayed. This motivates the use of learned forecasting models for predicting the evolving consumption state, together with data assimilation methods for sequential forecast correction. In this work, we study a high-dimensional data assimilation problem for real energy-consumption data. modeltextThe forward prediction is supplied by a pretrained black-box spatio-temporal forecasting model, which is treated as the state propagator in the filtering procedure. We employ the Ensemble Score Filter (EnSF) to assimilate partial and noisy observations and to correct the forecast trajectory over time. The EnSF uses score-based diffusion models to approximate filtering distributions and avoids retraining neural-network score models during assimilation by using a closed-form score representation and Monte Carlo approximation. Numerical experiments demonstrate that open-loop propagation of the learned forecasting model can become unreliable over long horizons, while EnSF-based correction substantially improves state estimation. Comparisons with the Ensemble Kalman Filter (EnKF) further show that EnSF provides stronger correction under the nonlinear observation setting considered in this work.