Diffusion bonding is a key manufacturing process for nucleation applications including compact heat exchangers. Accurately predicting the alloy's behavior during the diffusion bonding process presents challenges, primarily due to the intricate interplay of microstructural evolution and physical processes such as compressive loading, temperature history, and component migration. The current study develops a phase-field model designed to simulate the diffusion bonding in 316H stainless steel, a material with exceptional high-temperature strength, corrosion resistance and suitability to high-pressure conditions. Our model incorporates a multi-phase, multi-component framework that aligns the experimental observations with the grain growth and heterogeneous nucleation, where arbitrary external compressive load and temperature history are considered. The simulations focus on grain nucleation, growth, and microstructure evolutions across diffusion bonding line under a variety of temperature profiles, mechanical loads, and surface roughness conditions, mirroring experimental setups. Our model predicts consistent simulation results with experiments in terms of the grain size and distribution near the bonding area, offering a better understanding of the diffusion bonding mechanism and the manufacturing process for building reliable compact heat exchangers.