Incorporating microscopic details into fluctuating hydrodynamics has long been a challenge, as conventional top-down approaches often fail to capture the full spectrum of hydrodynamic interactions and fluctuations arising from microscopic physics. Dean and Kawasaki tackled this challenge by deriving a stochastic partial differential equation for density operators from microscopic Brownian processes; however, its mathematically ill-defined nature has posed significant obstacles for numerical implementations to sample field-theoretic dynamics. In this talk, I will introduce a mathematically regularized framework that overcomes these challenges and present a mesoscopic coarse-graining methodology to construct mesoscopic fields from microscopic molecules in terms of interactions and correlations. I will also demonstrate numerical implementation for weakly interacting molecular liquids at the mesoscopic field level. Even though mesoscopic interactions and correlations are integrated away during coarse-graining, the proposed approach effectively captures the temporal evolution of coarse-grained microscopic density profiles.