We present a novel method that integrates subspace modeling with an adaptive generative image prior for high-dimensional MR image reconstruction. The subspace model imposes an explicit low-dimensional representation of the high-dimensional images, while the generative image prior serves as a spatial constraint on the "contrast-weighted" images or the spatial coefficients of the subspace model. A formulation was introduced to synergize these two components with complimentary regularization such as joint sparsity. A special pretraining plus subject-specific network adaptation strategy was proposed to construct an accurate generative-model-based representation for images with varying contrasts, validated by experimental data. An iterative algorithm was introduced to jointly update the subspace coefficients and the multiresolution latent space of the generative image model that leveraged a recently developed intermediate layer optimization technique for network inversion. We evaluated the utility of the proposed method in two high-dimensional imaging applications: accelerated MR parameter mapping and high-resolution MRSI. Improved performance over state-of-the-art subspace-based methods was demonstrated in both cases. Our work demonstrated the potential of integrating data-driven and adaptive generative models with low-dimensional representation for high-dimensional imaging problems.

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