Stochastic dual dynamic programming (SDDP) is a widely used method for solving large-scale multi-stage stochastic linear programming problems arising for example in hydro-thermal scheduling problems. SDDP introduces scenario sampling to the nested Benders decomposition method. However, in its classical form SDDP relies heavily on the assumption of interstage independent random vectors so that Benders cuts can be shared among different scenarios at the same stage. In many practical applications this assumption might not be satisfied. Therefore, recently cut sharing has been generalized to linear or at least convex interstage dependent uncertainty in the right-hand side of the problem. We build upon this work and further generalize the cut-sharing methodology to a broader class of nonlinear uncertainty models. A real-life power system example is examined to illustrate the effectiveness of the proposed techniques.