This paper presents a novel method to reconstruct and separate metabolite and macromolecule (MM) signals in 1 H magnetic resonance spectroscopic imaging (MRS I) data using learned nonlinear models. Specifically, deep autoencoder (DAE) networks were constructed and trained to learn the nonlinear low-dimensional manifolds, where the metabolite and MM signals reside individually. A regularized reconstruction formulation is proposed to integrate the learned models with signal encoding model to reconstruct and separate the metabolite and MM components. An efficient algorithm was developed to solve the associated optimization problem. The performance of the proposed method has been evaluated using simulation and experimental 1 H-MRSI data. Efficient low-dimensional signal representation of the learned models and improved metabolite/MM separation over the standard parametric fitting based approach have been demonstrated.