Processes of scalar and vector fields (temperature, particle number density, magnetic field etc.) propagation in compressible strongly turbulent media are considered. The integral equation of the fields transportation and its diffusion approximation are obtained. The diffusion coefficient and corresponding coefficient of magnetic field generation (α-effect) are expressed in terms of the velocity correlators. The correlators of high rank are taken into account. A new mathematical approach is suggested which allows the theory to extend up to the large Strouhal number. It is shown that the turbulent diffusion coefficient can be negative, which implies the clustering of the admixture particles in patches (the local increasing of the temperature and magnetic fields). Explicit expressions for correlators of the scalar fields in turbulent media are obtained.