Magnetic diffusion plays an important role in inertial confinement fusion with strong magnetic fields. In this paper, we improve a previous analysis of the generation and diffusion of the magnetic field [Morita et al., Phys. Plasmas 25, 094505 (2018)]. For the generation process, we calculate the temporal evolution of the coil current using a self-consistent circuit model. The results show that the peak of the calculated magnetic field is delayed by 1.2 ns compared with that of the incident laser pulse. For the diffusion process, we evaluate the electrical conductivity of warm dense gold over a wide temperature range (300 K–100 eV) by combining the Kubo–Greenwood formula based on a quantum molecular dynamics simulation with the modified Spitzer model. Our simulation shows that the maximum magnetic field (530 T) that penetrates the cone is delayed by 2.5 ns compared with the laser peak. This result is consistent with experiments [Sakata et al., Nat. Commun. 9, 3937 (2018)] that showed that applying a strong magnetic field improved the heating efficiency of fusion fuel.