In dynamic biological processes such as development, spatial transcriptomics is revolutionizing the study of the mechanisms underlying spatial organization within tissues. Inferring cell fate trajectories from spatial transcriptomics profiled at several time points has thus emerged as a critical goal, requiring novel computational methods. Wasserstein gradient flow learning is a promising framework for analyzing sequencing data across time, built around a neural network representing the differentiation potential. However, existing gradient flow learning methods cannot analyze spatially resolved transcriptomic data.

Here, we propose STORIES, a method that employs an extension of Optimal Transport to learn a spatially informed potential. We benchmark our approach using three large Stereo-seq spatiotemporal atlases and demonstrate superior spatial coherence compared to existing approaches. Finally, we provide an in-depth analysis of axolotl neural regeneration and mouse gliogenesis, recovering gene trends for known markers as Nptx1 in neuron regeneration and Aldh1l1 in gliogenesis and additional putative drivers.