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Abstract Spatial transcriptomics (ST) technologies measure gene expression at thousands of locations within a two-dimensional tissue slice, enabling the study of spatial gene expression patterns. Spatial variation in gene expression is characterized byspatial gradients, or the collection of vector fields describing the direction and magnitude in which the expression of each gene increases. However, the few existing methods that learn spatial gradients from ST data either make restrictive and unrealistic assumptions on the structure of the spatial gradients or do not accurately model discrete transcript locations/counts. We introduce SLOPER (for Score-based Learning Of Poisson-modeled Expression Rates), a generative model for learning spatial gradients (vector fields) from ST data. SLOPER models the spatial distribution of mRNA transcripts with aninhomogeneous Poisson point process (IPPP)and usesscore matchingto learn spatial gradients for each gene. SLOPER utilizes the learned spatial gradients in a novel diffusion-based sampling approach to enhance the spatial coherence and specificity of the observed gene expression measurements. We demonstrate that the spatial gradients and enhanced gene expression representations learned by SLOPER leads to more accurate identification of tissue organization, spatially variable gene modules, and continuous axes of spatial variation (isodepth) compared to existing methods. Software availabilitySLOPER is available athttps://github.com/chitra-lab/SLOPER.