We introduce the state-of-the-art deep learning Denoising Diffusion Probabilistic Model (DDPM) as a method to infer the volume or number density of giant molecular clouds (GMCs) from projected mass surface density maps. We adopt magnetohydrodynamic simulations with different global magnetic field strengths and large-scale dynamics, i.e., noncolliding and colliding GMCs. We train a diffusion model on both mass surface density maps and their corresponding mass-weighted number density maps from different viewing angles for all the simulations. We compare the diffusion model performance with a more traditional empirical two-component and three-component power-law fitting method and with a more traditional neural network machine learning approach (CASI-2D). We conclude that the diffusion model achieves an order of magnitude improvement on the accuracy of predicting number density compared to that by other methods. We apply the diffusion method to some example astronomical column density maps of Taurus and the Infrared Dark Clouds (IRDCs) G28.37+0.07 and G35.39-0.33 to produce maps of their mean volume densities.

翻译：我们引入最先进的深度学习去噪扩散概率模型（DDPM），作为从投影质量表面密度图中推断巨分子云（GMC）体积密度或数密度的方法。我们采用具有不同全局磁场强度和大尺度动力学（即非碰撞与碰撞GMC）的磁流体动力学模拟。针对所有模拟，我们从不同视角训练扩散模型，其输入为质量表面密度图及其对应的质量加权数密度图。我们将扩散模型的性能与更传统的双分量和三分量幂律拟合方法，以及传统的神经网络机器学习方法（CASI-2D）进行比较。结论表明，与其他方法相比，扩散模型在预测数密度精度上实现了数量级的提升。我们将扩散方法应用于金牛座及红外暗云（IRDC）G28.37+0.07和G35.39-0.33的示例天文柱密度图，生成了其平均体积密度图。