This paper is concerned with the diffusive expansion for solutions of the rescaled Boltzmann equation in the whole space (0.1) ϵ ∂ t F ϵ + v ⋅ ∇ x F ϵ = 1 ϵ Q ( F ϵ , F ϵ ) , x ∈ R N , v ∈ R N , t > 0 , with prescribed initial data (0.2) F ϵ ( t , x , v ) | t = 0 = F 0 ϵ ( x , v ) , x ∈ R N , v ∈ R N . Our main purpose is to justify the global validity of the diffusive expansion (0.3) F ϵ ( t , x , v ) = μ + μ { ϵ f 1 ( t , x , v ) + ϵ 2 f 2 ( t , x , v ) + ⋯ + ϵ n − 1 f n − 1 ( t , x , v ) + ϵ n f n ϵ ( t , x , v ) } for a solution F ϵ ( t , x , v ) of the rescaled Boltzmann equation (0.1) in the whole space R N for all t ⩾ 0 with initial data F 0 ϵ ( x , v ) satisfying the initial expansion (0.4) F 0 ϵ ( x , v ) = μ + μ { ϵ f 1 ( 0 , x , v ) + ϵ 2 f 2 ( 0 , x , v ) + ⋯ + ϵ n − 1 f n − 1 ( 0 , x , v ) + ϵ n f n ϵ ( 0 , x , v ) } , ( x , v ) ∈ R 2 N . Here μ ( v ) = ( 2 π ) − N 2 exp ( − | v | 2 2 ) is a normalized global Maxwellian. Under the assumption that the fluid components of the coefficients f m ( 0 , x , v ) ( 1 ⩽ m ⩽ n ) of the initial expansion F 0 ϵ ( x , v ) have divergence-free velocity fields u m 0 ( x ) as well as temperature fields θ m 0 ( x ) , if we assume further that the velocity-temperature fields [ u 1 0 ( x ) , θ 1 0 ( x ) ] of f 1 ( 0 , x , v ) have small amplitude in H s ( R N ) ( s ⩾ 2 ( N + n + 2 ) ) , we can determine these coefficients f m ( t , x , v ) ( 1 ⩽ m ⩽ n ) in the diffusive expansion (0.3) uniquely by an iteration method and energy method. The hydrodynamic component of these coefficients f m ( t , x , v ) ( 1 ⩽ m ⩽ n ) satisfies the incompressible condition, the Boussinesq relations and/or the Navier–Stokes–Fourier system respectively, while the microscopic component of these coefficients is determined by a recursive formula. Compared with the corresponding problem inside a periodic box studied in Y. Guo (2006) [18], the main difficulty here is due to the fact that Poincaré's inequality is not valid in the whole space R N and this difficulty is overcome by using the L p – L q -estimate on the Riesz potential. Moreover, by exploiting the energy method, we can also deduce certain the space–time energy estimates on these coefficients f m ( t , x , v ) ( 1 ⩽ m ⩽ n ) . Once the coefficients f m ( t , x , v ) ( 1 ⩽ m ⩽ n ) in the diffusive expansion (0.3) are uniquely determined and some delicate estimates have been obtained, the uniform estimates with respect to ϵ on the remainders f n ϵ ( t , x , v ) are then established via a unified nonlinear energy method and such an estimate guarantees the validity of the diffusive expansion (0.3) in the large provided that (0.5) N > 2 n + 2 . Notice that for m ⩾ 2 , u m ( t , x ) is no longer a divergence-free vector and it is worth to pointing out that, for m ⩾ 3 , it was in deducing certain estimates on p m ( t , x ) by the L p – L q -estimate on the Riesz potential that we need to require that N > 2 n + 2 .