It is shown that various multicomponent diffusion equations can be written in the generalized Maxwell-Stefan (MS) form by using a simple generalization of the inversion method presented in a publication by Merk [1959. Applied Scientific Research A 8, 73-99]. The new approach can be considered a reformulation of the Curtiss-Bird inversion [1999. Industrial & Engineering Chemistry Research 38(7), 2515-2522], but it is simpler and more versatile-it can be used to invert the Onsager-Fuoss, Darken, Nernst-Planck, and generalized Fick equations; and to provide expressions for the MS diffusivities without making assumptions about the diagonal MS diffusivities. This approach complements the reversion described by Taylor and Krishna, which changes the MS equations to the form of the generalized Fick equations. As a detailed example, the Lattice Density Functional Theory (LDFT) equations for diffusion in a quaternary system are inverted to MS form by using the new approach; in addition, the resultant MS equations are reverted to the generalized Fick form by using the approach of Taylor and Krishna; last, the original LDFT equations are retrieved by using a priori information from the new approach. This example demonstrates the straightforwardness of switching between various forms of any diffusion equation. Additionally, the example ascertains that the MS diffusivities are symmetric and always positive, at least when obtained from the near-equilibrium LDFT equations at low density-this builds on the works of Curtiss and Bird [1999. Industrial & Engineering Chemistry Research 38(7), 2515-2522] and Condiff [1969. Journal of Chemical Physics 51(10) 4209] that demonstrate only the symmetry, and it offers an alternative explanation for the observance of negative MS diffusivities. (c) 2005 Elsevier Ltd. All rights reserved.