Classical phenomenological model of diffusion in fluids is based on the concept of the mean-free-path, λ , and density distribution, n ( x , t ) , as a function of coordinate, x , and time, t . Under the assumption that (1) n ( x - λ , t ) - n ( x + λ , t ) ≈ - 2 λ ( ∂ n / ∂ x ) , this model results in the classical diffusion equation, (2) ∂ n ( x , t ) ∂ t = ∂ ∂ x D ∂ n ( x , t ) ∂ x , where (3) D = ( 1 / 3 ) V ¯ λ and V ¯ is the average velocity of molecules. However, Eq. (3) implies finite λ , but approximation (1) requires the limit of λ → 0 . Here we show that this (mean-free-path) inconsistency distorts the essential physics; in particular, it results in wrong solutions at finite and large λ (including an incorrect limit for the ideal gas). In this paper, the mean-free-path inconsistency is corrected by relaxing the unnecessary assumption (1). This gives a finite-difference equation for the classical diffusion model: (4) ∂ n ( x , t ) ∂ t = ∂ ∂ x D 2 λ [ n ( x + λ , t ) - n ( x - λ , t ) ] and its generalization taking into account statistical distribution of free-path lengths: (5) ∂ n ( x , t ) ∂ t = ∂ ∂ x D 2 λ 2 ∫ 0 ∞ [ n ( x + ξ , t ) - n ( x - ξ , t ) ] exp - ξ λ d ξ . We have solved and analyzed Eqs. (4) and (5) for capturing boundaries, for infinite system without boundaries, and for periodic initial conditions. Our analysis indicates that these new equations allow more accurate calculations for the classical model and predict new elements of diffusion mechanisms in fluids, such as diffusion correlations.