The recently developed conditional Gaussian diffusion process model is a powerful tool of survival analysis. Its generality not only encompasses the survival models to date but also brings into focus the influence of unobserved variables related to "death" of individuals. Further, that the model makes feasible a unique estimation of the parameters of the underlying unobserved or partially observed process is shown in this paper through a set of simulated data on death times and an unobserved variable. Possibilities of extensive use of the model to areas other than mortality are pointed out.