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Multiplexed RNA sequencing in individual cells is transforming basic and clinical life sciences^{, , –}. Often, however, tissues must first be dissociated, and crucial information about spatial relationships and communication between cells is thus lost. Existing approaches to reconstruct tissues assign spatial positions to each cell, independently of other cells, by using spatial patterns of expression of marker genes^,—which often do not exist. Here we reconstruct spatial positions with little or no prior knowledge, by searching for spatial arrangements of sequenced cells in which nearby cells have transcriptional profiles that are often (but not always) more similar than cells that are farther apart. We formulate this task as a generalized optimal-transport problem for probabilistic embedding and derive an efficient iterative algorithm to solve it. We reconstruct the spatial expression of genes in mammalian liver and intestinal …