In this paper we consider the model of turbulent diffusion of a passive scalar field in a compressible turbulent flow. The velocity field is modeled by the Kazantsev–Kraichnan “rapid-change” ensemble, while the scalar density field is described by a strongly nonlinear stochastic advection-diffusion equation. As a requirement of renormalizability, the model necessarily involves infinite number of coupling constants. Despite this fact, it is possible to use the renormalization group technique. Renormalization group equations reveal existence of two-dimensional surfaces of fixed points in the infinite-dimensional space of couplings. If some areas on these surfaces involve infrared attractive regions, the problem allows for the large-scale, long-time scaling behaviour. Critical dimensions of the fields and parameters and the spreading law for the particle’s cloud are derived for different scaling regimes.