Spatial transcriptomics (ST) profiles gene expression in intact tissues. However, ST data measured at each spatial location may represent gene expression of multiple cell types, making it difficult to identify cell-type-specific transcriptional variation across spatial contexts. Existing cell-type deconvolutions of ST data often require single-cell transcriptomic references, which can be limited by availability, completeness and platform effect of such references. We present RETROFIT, a reference-free Bayesian method that produces sparse and interpretable solutions to deconvolve cell types underlying each location independent of single-cell transcriptomic references. Results from synthetic and real ST datasets acquired by Slide-seq and Visium platforms demonstrate that RETROFIT outperforms existing reference-based and reference-free methods in estimating cell-type composition and reconstructing gene expression. Applying RETROFIT to human intestinal development ST data reveals spatiotemporal patterns of cellular composition and transcriptional specificity. RETROFIT is available at https://bioconductor.org/packages/release/bioc/html/retrofit.html.