Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. However, there is currently a lack of general techniques that can jointly fuse multiple data sets with varying fidelity levels while also estimating calibration parameters. To address this gap, we introduce a novel approach that, using latent-map Gaussian processes (LMGPs), converts data fusion into a latent space learning problem where the relations among different data sources are automatically learned. This conversion endows our approach with some attractive advantages such as increased accuracy and reduced overall costs compared to existing techniques that need to take a combinatorial approach to fuse multiple datasets. Additionally, we have the flexibility to jointly fuse any number of data sources and the ability to visualize correlations between data sources. This visualization allows an analyst to detect model form errors or determine the optimum strategy for high-fidelity emulation by fitting LMGP only to the sufficiently correlated data sources. We also develop a new kernel that enables LMGPs to not only build a probabilistic multi-fidelity surrogate but also estimate calibration parameters with quite a high accuracy and consistency. The implementation and use of our approach are considerably simpler and less prone to numerical issues compared to alternate methods. Through analytical examples, we demonstrate the benefits of learning an interpretable latent space and fusing multiple (in particular more than two) sources of data.