The performance of machine learning surrogates is critically dependent on data quality and quantity. This presents a major challenge, as high-fidelity (HF) data is often scarce and computationally expensive to acquire, while low-fidelity (LF) data is abundant but less accurate. To address this data scarcity problem, we develop a probabilistic multi-fidelity surrogate framework based on generative transfer learning. We employ a normalizing flow (NF) generative model as the backbone, which is trained in two phases: (i) the NF is first pretrained on a large LF dataset to learn a probabilistic forward model; (ii) the pretrained model is then fine-tuned on a small HF dataset, allowing it to correct for LF-HF discrepancies via knowledge transfer. To relax the dimension-preserving constraint of standard bijective NFs, we integrate surjective (dimension-reducing) layers with standard coupling blocks. This architecture enables learned dimension reduction while preserving the ability to train with exact likelihoods. The resulting surrogate provides fast probabilistic predictions with quantified uncertainty and significantly outperforms LF-only baselines while using fewer HF evaluations. We validate the approach on a reinforced concrete slab benchmark, combining many coarse-mesh (LF) simulations with a limited set of fine-mesh (HF) simulations. The proposed model achieves probabilistic predictions with HF accuracy, demonstrating a practical path toward data-efficient, generative AI-driven surrogates for complex engineering systems.