This study aims to provide fundamental understandings of the pressure effects on the soot formation and compare the performances of different soot aerosol models. Numerical simulations are performed in laminar coflow diffusion flames at pressures ranging from 1 to 16 bar. Two soot aerosol models are considered: the acetylene-based semi-empirical (SE) model and polycyclic aromatic hydrocarbons (PAH) based hybrid method of moment (HMOM). To study the effect of large-sized PAH species, a detailed reaction mechanism is used with PAH pathways up to coronene. Results show that the SE model provides good predictions of pressure scaling of peak soot mass with a deviation of 7%, while HMOM obtains better soot predictions on the flame centerline. Due to the shifting of PAH position towards the burner with increasing pressure, the nascent soot is formed earlier. The increase in the particle residence time is found to be an additional factor that further promotes the increased soot formation with pressure, apart from the increase in density, temperature, and PAH concentration. The residence time at 8 bar case is 2.5 times and 3.0 times longer than those at 1 bar case on the flame centerline and flame wings, respectively. Moreover, the pressure effects on the PAH contribution to the nucleation process are studied. Although small-sized PAH species (A2 and A2R5) dominate the nucleation process, the contribution of large-sized PAH species (larger than A4) increases from 5% to 20% of the total on the flame wings, when the pressure increases from 1 bar to 8 bar.