Elucidated Rolling Diffusion Models for Probabilistic Weather Forecasting

2025-06-24

AI Summary

Existing probabilistic forecasting methods for high-dimensional chaotic systems suffer from inadequate temporal dependency modeling and fail to explicitly characterize the growth of uncertainty with forecast horizon. Method: This paper proposes a novel rolling diffusion forecasting framework. Its core innovations include: (i) the first integration of Elucidated Diffusion Models (EDM) into the rolling prediction paradigm; (ii) a medium-range-forecast-oriented loss weighting strategy and an efficient initialization method leveraging pre-trained models; and (iii) a hybrid sequence architecture unifying spatiotemporal feature extraction with conditional diffusion modeling, enhanced by an improved noise schedule, network pre-conditioning, and the Heun sampler. Results: Evaluated on 2D Navier–Stokes simulations and the ERA5 weather forecasting benchmark, the method significantly outperforms state-of-the-art diffusion-based baselines—including conditional autoregressive EDM—achieving superior fidelity, robustness, and generalization across diverse forecasting horizons.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Planning, Routing, and Scheduling: Planning with Language Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Diffusion models are a powerful tool for probabilistic forecasting, yet most applications in high-dimensional chaotic systems predict future snapshots one-by-one. This common approach struggles to model complex temporal dependencies and fails to explicitly account for the progressive growth of uncertainty inherent to such systems. While rolling diffusion frameworks, which apply increasing noise to forecasts at longer lead times, have been proposed to address this, their integration with state-of-the-art, high-fidelity diffusion techniques remains a significant challenge. We tackle this problem by introducing Elucidated Rolling Diffusion Models (ERDM), the first framework to successfully unify a rolling forecast structure with the principled, performant design of Elucidated Diffusion Models (EDM). To do this, we adapt the core EDM components-its noise schedule, network preconditioning, and Heun sampler-to the rolling forecast setting. The success of this integration is driven by three key contributions: (i) a novel loss weighting scheme that focuses model capacity on the mid-range forecast horizons where determinism gives way to stochasticity; (ii) an efficient initialization strategy using a pre-trained EDM for the initial window; and (iii) a bespoke hybrid sequence architecture for robust spatiotemporal feature extraction under progressive denoising. On 2D Navier-Stokes simulations and ERA5 global weather forecasting at 1.5^circ resolution, ERDM consistently outperforms key diffusion-based baselines, including conditional autoregressive EDM. ERDM offers a flexible and powerful general framework for tackling diffusion-based sequence generation problems where modeling escalating uncertainty is paramount. Code is available at: https://github.com/salvaRC/erdm

Problem

• Modeling complex temporal dependencies in probabilistic weather forecasting
• Integrating rolling diffusion with high-fidelity techniques for uncertainty growth
• Improving accuracy in mid-range forecast horizons with novel loss weighting

Innovation

• Unified rolling forecast with Elucidated Diffusion Models
• Novel loss weighting for mid-range forecast horizons
• Hybrid sequence architecture for spatiotemporal feature extraction