An enduring evolutionary puzzle is the question of why some animals have high cell diversity (such as humans, who possess at least 500 hundred morphologically distinct types of cells), while others have lower diversity (such as Trichoplax adhaerens, which has 6 to 30 morphologically distinct cell types). Here I present a phylogenetic analysis of the tempo and mode of cell type evolution. I have constructed cell phylogenies, where the taxa are cells and characters are gene expression. This was achieved by transforming single cell RNAseq abundance data to a gaussian distribution, allowing us to leverage existing models of continuous trait evolution for phylogenetic inference. To study the origin of cellular dynamics, I concentrate my analyses on a key position of the animal tree – the four non-bilaterian clades (Ctenophora, Porifera, Placozoa and Cnidaria) – investigating a species from each. I examine the geometry of these cell phylogenies to determine the overall tempo of cell type evolution in each species, and ask whether diversity in the rate of cell type diversification underlies the variation in cell richness seen across species. I find that while rates of loss are constant and low, the four non-bilaterian species have varying cell diversification rates which, in all species, decline over evolutionary time. By investigating the tempo and mode of cell type evolution, I hope to shed light on the origins of animal diversity.