Diffusion Modeling of the Three-Dimensional Magnetic Field in the Sun's Corona

In this work, we introduce a novel generative denoising diffusion model for synthesizing the Sun's three-dimensional coronal magnetic field, a complex and dynamic region characterized by evolving magnetic structures. Despite daily variability, these structures exhibit recurring patterns and long-term cyclic trends, presenting unique modeling challenges and opportunities at the intersection of physics and machine learning. Our generative approach employs an innovative architecture influenced by Spherical Fourier Neural Operators (SFNO), operating within the spherical harmonic domain, where the scalar field corresponds directly to the magnetic potential under physical constraints. We trained this model using an extensive dataset comprising 11.7 years of daily coupled simulations from the Air Force Data Assimilative Photospheric Flux Transport-Wang Sheeley Arge (ADAPT-WSA) model, further enhanced by data augmentation. Initial results demonstrate the model's capability to conditionally generate physically realistic magnetic fields reflective of distinct phases within the 11-year solar cycle: from solar minimum ($S = 0$) to solar maximum ($S = 1$). This approach represents a significant step toward advanced generative three-dimensional modeling in Heliophysics, with potential applications in solar forecasting, data assimilation, inverse problem-solving, and broader impacts in areas such as procedural generation of physically-informed graphical assets.