Predicting partially observable dynamical systems via diffusion models with a multiscale inference scheme

TL;DR

The paper tackles probabilistic forecasting of partially observable, long-memory dynamical systems using diffusion models. It introduces a multiscale inference scheme built on time-temporal templates that condition on both distant past and present information, enabling long-horizon predictions without increasing computational cost. Across synthetic and real solar-dynamics data, the method reduces bias, improves rollout stability, and outperforms autoregressive and Hierarchy-2 baselines, while delivering a new 8.5TB multi-modal solar dataset for future benchmarking. The work highlights the value of multiscale temporal conditioning for physics-informed forecasting and points to adaptive conditioning as a promising avenue for future improvement.

Abstract

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at a given time represents only a small fraction of what is needed to predict future states, either due to measurement uncertainty or because only a small fraction of the state can be observed. This is true for example in solar physics, where we can observe the Sun's surface and atmosphere, but its evolution is driven by internal processes for which we lack direct measurements. In this paper, we tackle the probabilistic prediction of partially observable, long-memory dynamical systems, with applications to solar dynamics and the evolution of active regions. We show that standard inference schemes, such as autoregressive rollouts, fail to capture long-range dependencies in the data, largely because they do not integrate past information effectively. To overcome this, we propose a multiscale inference scheme for diffusion models, tailored to physical processes. Our method generates trajectories that are temporally fine-grained near the present and coarser as we move farther away, which enables capturing long-range temporal dependencies without increasing computational cost. When integrated into a diffusion model, we show that our inference scheme significantly reduces the bias of the predicted distributions and improves rollout stability.

Figures (14)

• Figure 1: Multiscale templates and inference scheme.(Left): Our multiscale templates in purple. (Right): Comparing a standard autoregressive scheme (on top) with our multiscale inference scheme. We use the visualization style of harvey2022flexible, in which dark boxes indicate available steps (either observed or generated at previous iterations) and red and blue boxes indicate steps that are used as conditioning or generated, respectively. Each row is a new call to the conditional diffusion model with the used template indicated by the number next to the row. Our inference scheme enables capturing longer-range dependencies, conditions more often in the past, and mitigate rollout instability by generating a distant future ($9$ on the figure) in one call to the conditional diffusion model.
• Figure 2: Performance of our multiscale inference scheme on a synthetic example. The observed data (blue) consists of Gaussian fluctuations around a sinusoidal trend. Predictions (red) are from a diffusion model with access only to past data $t\leq0$. (Top): The global trend is barely observable at fine scale. Thus, a model that generates small trajectory segments autoregressively tends to accumulate errors, leading to biased and overly broad predicted distributions. (Bottom): Our multiscale inference scheme (see Fig. \ref{['fig:illustration']}) efficiently recovers the target distribution -- with a Wasserstein distance of 0.021 vs. 0.23 for the autoregressive model. When restricted to the same 3-step past horizon, the multiscale inference still performs better, with a Wasserstein distance of 0.08.
• Figure 3: (Above): Example full-disk solar images from 2015-12-12 (see § \ref{['sec:solardynamics']} for details). The left three panels are photospheric vector magnetic-field components; the right three panels are images of the solar corona and chromosphere. "Active regions" (intense magnetic fields connected to bright coronal structures) are present in both modalities. (Below): A sequence of frames of a cropped active region, corresponding to the red box in the row above.
• Figure 4: Example of predictions, for different inference schemes: autoregressive and multiscale (ours). Colorbar: -3000 3000 Gauss (magnetic field).
• Figure 5: Solar activity. The standard deviation of the $B_{\rm r}$ component over the full solar disk as a proxy for solar activity, illustrating the temporal segmentation used for model development. The dataset is divided into training (blue), validation (yellow), and test (green) intervals, with each evaluation segment separated from training data by at least one full month. The split ensures disjoint active regions across sets and includes test intervals during both high and low solar activity, enabling robust model evaluation across varying solar conditions.