Employing a widely used model for the dynamics of irreversible processes, we introduce curvature into the Euclidean state space of fluctuating irreversible processes in (quasi-)linear domains via nonintegrable coordinate transformations. The Riemannian state space thus obtained pertains to the nonlinear domain of far from equilibrium situations. This technique makes it possible to extend systematically, without the need for adding stochastic assumptions, both the path integral expression for the conditional probability and the Fokker-Planck equation, from (quasi-)linear to nonlinear regimes. Our results agree with those obtained by Grabert and Green (1979) which are based on stochastic considerations. The connection with other rigorous results in the literature is also discussed.