Fast probabilistic galaxy field generation with diffusion models

In the era of precision cosmology, the ability to generate accurate and large-scale galaxy catalogs is crucial for advancing our understanding of the universe. With the flood of cosmological data from current and upcoming missions, generating theoretical predictions to compare with these observations is essential for constraining key cosmological parameters. While traditional methods, such as the Halo-Occupation Distribution (HOD), have provided foundational insights, they struggle to balance the need for both accuracy and computational efficiency. High-fidelity hydrodynamic simulations offer improved precision but are computationally prohibitive. In this work, we introduce a novel machine learning approach that harnesses Convolutional Neural Networks (CNNs) and diffusion models, trained on the CAMELS simulation suite, to bridge the gap between computationally inexpensive dark matter simulations and the galaxy distributions of more costly hydrodynamic simulations. Our method not only outperforms traditional HOD techniques in accuracy but also significantly accelerates the simulation process, offering a scalable solution for next-generation cosmological surveys. This advancement has the potential to revolutionize galaxy catalog generation, enabling more precise, data-driven cosmological analyses.