  Spatial transcriptomics data is invaluable for understanding the spatial
organization of gene expression in tissues. There have been consistent efforts
in studying how to effectively utilize the associated spatial information for
refining gene expression modeling. We introduce a class of distance-preserving
generative models for spatial transcriptomics, which utilizes the provided
spatial information to regularize the learned representation space of gene
expressions to have a similar pair-wise distance structure. This helps the
latent space to capture meaningful encodings of genes in spatial proximity. We
carry out theoretical analysis over a tractable loss function for this purpose
and formalize the overall learning objective as a regularized evidence lower
bound. Our framework grants compatibility with any variational-inference-based
generative models for gene expression modeling. Empirically, we validate our
proposed method on the mouse brain tissues Visium dataset and observe improved
performance with variational autoencoders and scVI used as backbone models.
