The transport of charged particles in various astrophysical environments permeated by magnetic fields is described in terms of a diffusion process, which relies on diffusion-tensor parameters generally inferred from Monte-Carlo simulations. Based on a red-noise approximation to model the two-point correlation function of the magnetic field experienced by charged particles between two successive times, the diffusion-tensor coefficients were previously derived in the case of pure turbulence. In this contribution to ECRS2022, the derivation is extended to the case of a mean field on top of the turbulence. The results are applicable to a variety of astrophysical environments in regimes where the Larmor radius of the particles is resonant with the power spectrum of the turbulence wavelength (gyro-resonant regime), or where the Larmor radius is greater than the largest turbulence wavelength (high-rigidity regime).