Exploring Magnetic Fields in Molecular Clouds through Denoising Diffusion Probabilistic Models

Abstract Accurately measuring magnetic field strength in the interstellar medium, including giant molecular clouds, remains a significant challenge. We present a machine learning approach using denoising diffusion probabilistic models (DDPMs) to estimate magnetic field strength from synthetic observables such as column density, orientation angles of the dust continuum polarization vector, and line-of-sight (LOS) nonthermal velocity dispersion. We trained three versions of the DDPM model: the 1-channel DDPM (using only column density), the 2-channel DDPM (incorporating both column density and polarization angles), and the 3-channel DDPM (which combines column density, polarization angles, and LOS nonthermal velocity dispersion). The code and trained model are available on GitHub at https://github.com/xuduo117/DDPM_Bmag . We assessed the models on both synthetic test samples and new simulation data that were outside the training set's distribution. The 3-channel DDPM consistently outperformed both the other DDPM variants and the power-law fitting approach based on column density alone, demonstrating its robustness in handling previously unseen data. Additionally, we compared the performance of the Davis–Chandrasekhar–Fermi (DCF) methods, both classical and modified, to the DDPM predictions. The classical DCF method overestimated the magnetic field strength by approximately an order of magnitude. Although the modified DCF method showed improvement over the classical version, it still fell short of the precision achieved by the 3-channel DDPM.