we consider a class of parametric regression problems where the signal is observed through random nonlinear functions with a difference of convex (dc) form. this model describes a broad subset of nonlinear regression problems that includes familiar special cases such as phase retrieval/quadratic regression and blind deconvolution/bilinear regression. given the dc decomposition of the observation functions as well as an approximate solution, we formulate a convex program as an estimator that operates in the natural space of the signal. our approach is computationally superior to the methods based on semidefinite/sum-of-squares relaxation---tailored for polynomial observation functions---and can compete with the non-convex methods studied in special regression problems. furthermore, under mild moment assumptions, we derive the sample complexity of the proposed convex estimator using a pac-bayesian argument. we instantiate our results with bilinear regression with gaussian factors and provide a method for constructing the required initial approximate solution.