A family of sufficient dimension reduction methods, called inverse regression, commonly require the linearity condition that E(X|B'X) must be a linear function of B'X and the constant variance condition that var(X|B'X) must be degenerate for certain B. In this paper, we relax these conditions by allowing more flexibility on the functional forms of E(X|B'X) and var(X|B'X), under the assumption on the existence of a latent variable that generates X. The generalized conditions are satisfied when X has a mixture elliptical or mixture Normal distribution, which is fairly general in practice. Under the relaxed conditions, we generalize the existing inverse regression methods, with additional adjustments that enhance the exhaustiveness of the methods. Efficient iterative algorithms are proposed for implementation, and simulation models and a real data example are studied to illustrate the effectiveness of the proposed methods.