Decoding spatial transcriptomes from single-cell RNA sequencing (scRNA-seq) data has become a fundamental technique for understanding multicellular systems; however, existing computational methods lack both accuracy and biological interpretability due to their model-free frameworks. Here, we introduce Perler, a model-based method to integrate scRNA-seq data with reference in situ hybridization (ISH) data. To calibrate differences between these datasets, we develop a biologically interpretable model that uses generative linear mapping based on a Gaussian mixture model using the Expectation-Maximization algorithm. Perler accurately predicts the spatial gene expression of Drosophila embryos, zebrafish embryos, mammalian liver, and mouse visual cortex from scRNA-seq data. Furthermore, the reconstructed transcriptomes do not over-fit the ISH data and preserved the timing information of the scRNA-seq data. These results demonstrate the generalizability of Perler for dataset integration, thereby providing a biologically interpretable framework for accurate reconstruction of spatial transcriptomes in any multicellular system.