Magnetic resonance spectroscopic imaging (MRSI) is a powerful tool capable of providing spatially localized maps of metabolite concentrations. Its utility, however, is often depreciated by spectral leakage artifacts resulting from low spatial resolution measurements through an effort to reduce acquisition times. Though model-based techniques can help circumvent these drawbacks, they require strong prior knowledge, and can introduce additional artifacts when the underlying models are inaccurate. We introduce a novel scheme in which a generative model is estimated from the raw MRSI data via a regularized variational framework that minimizes the model approximation error within a measurement-prescribed subspace. As additional a priori information, our approach relies only upon a measured field inhomogeneity map at high spatial resolution. We demonstrate the feasibility of our approach on both synthetic and experimental data.