Dynamic Diffusion Schrödinger Bridge in Astrophysical Observational Inversions

TL;DR

This work addresses inverse observational prediction in Giant Molecular Clouds by introducing Astro-DSB, a Dynamic Diffusion Schrödinger Bridge that directly maps observables to ground-truth physical states while respecting GMC dynamics. It removes the Gaussian prior, employs a paired boundary-matching scheme, and adds noise-alignment and observable-enhancement modules, along with patch-based training and aggregated sampling for scalability. The approach demonstrates robust ID and especially strong OOD generalization on simulated MHD data and shows promising qualitative agreement with real Taurus B213 observations, while achieving faster convergence and lower training costs than prior conditional DDPMs. The results highlight the value of distribution-level probabilistic modeling in physics-informed inference and suggest a path toward more interpretable, robust generative models for complex dynamical systems.

Abstract

We study Diffusion Schrödinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the Astro-DSB model, a variant of DSB with the pairwise domain assumption tailored for astrophysical dynamics. By investigating its learning process and prediction performance in both physically simulated data and in real observations (the Taurus B213 data), we present two main takeaways. First, from the astrophysical perspective, our proposed paired DSB method improves interpretability, learning efficiency, and prediction performance over conventional astrostatistical and other machine learning methods. Second, from the generative modeling perspective, probabilistic generative modeling reveals improvements over discriminative pixel-to-pixel modeling in Out-Of-Distribution (OOD) testing cases of physical simulations with unseen initial conditions and different dominant physical processes. Our study expands research into diffusion models beyond the traditional visual synthesis application and provides evidence of the models' learning abilities beyond pure data statistics, paving a path for future physics-aware generative models which can align dynamics between machine learning and real (astro)physical systems.

Figures (9)

• Figure 1: We introduce Astro-DSB for astrophysical inverse predictions from observables within Giant Molecular Clouds (GMCs). We visualize the observables, predicted results, and ground truth physical distributions on the density (top) and magnetic field (bottom) for in-distribution (ID) and out-of-distribution (OOD) testing cases, with the OOD defined via changes in initial physical conditions and dominant dynamical processes in the simulations.
• Figure 2: Illustration pipeline of our proposed Astro-DSB method. In the training stage, we propose to learn the DSB model under the pairwise matching assumption with observational noises alignment $\varepsilon$ and enhancement observables $\mathbf{y}$. In inference, we adopt an aggregated scalable sampling strategy to infer physical distributions from larger observables, such as Taurus B213.
• Figure 3: Multiple qualitative visualizations for relative error comparisons. (a) 2D histogram showing the distribution of ground truth (x-axis) versus predictions (y-axis). An accurate and unbiased prediction lies along the 1-to-1 diagonal line. (b) Relative error between the ground truth and predictions. (c) Residual maps showing the difference between model predictions and the ground truth across different methods. Results from Astro-DSB present more balanced and unbiased prediction error patterns compared to other ML methods, particularly for OOD testing cases. Best viewed in color and with zoom-in.
• Figure 4: Visualization of observables and our predicted results on Herschel column density map of Taurus B213, shown in the plane of the sky with the x-axis representing right ascension and the y-axis representing declination. The observable map is measured in $N_H /cm^{-2}$, and the prediction is in $n_H /cm^{-3}$. While there is no ground truth for real-world observations, our prediction results are consistent with those obtained with other independent approaches.
• Figure 5: Illustration of different synthetic observables from xu2025exploring for density and magnetic field estimation. Top left: map of column density with magnetic field directions; Top right: magnetic field angle dispersion; Bottom left: LOS velocity dispersion; Bottom right: projected magnetic field strength.