To develop a new method that integrates subspace and generative image models for high-dimensional MR image reconstruction. We proposed a formulation that synergizes a low-dimensional subspace model of high-dimensional images, an adaptive generative image prior serving as spatial constraints on the sequence of "contrast-weighted" images or spatial coefficients of the subspace model, and a conventional sparsity regularization. A special pretraining plus subject-specific network adaptation strategy was proposed to construct an accurate generative-network-based representation for images with varying contrasts. An iterative algorithm was introduced to jointly update the subspace coefficients and the multi-resolution latent space of the generative image model that leveraged an recently proposed intermediate layer optimization technique for network inversion. We evaluated the utility of the proposed method for two high-dimensional imaging applications: accelerated MR parameter mapping and high-resolution MR spectroscopic imaging. Improved performance over state-of-the-art subspace-based methods was demonstrated in both cases. The proposed method provided a new way to address high-dimensional MR image reconstruction problems by incorporating an adaptive generative model as a data-driven spatial prior for constraining subspace reconstruction. Our work demonstrated the potential of integrating data-driven and adaptive generative priors with canonical low-dimensional modeling for high-dimensional imaging problems.