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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 face challenges in analyzing spatially resolved transcriptomic data. Here, we propose STORIES, a method that uses 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 such as Nptx1 in neuron regeneration and Aldh1l1 in gliogenesis and additional putative drivers.

Fully capturing cellular identity requires integrating multiple molecular layers. Bridge integration, i.e. aligning unimodal datasets using a paired multi-omic reference, has emerged as a practical solution, yet existing methods offer limited interpretability and use paired information without regularization, making them sensitive to limited size and coverage. We introduce CHAMPOLLION, which uses regularized optimal transport to learn an interpretable cross-modal metric that drives the alignment of unpaired cells while capturing relationships between molecular features. Benchmarks on RNA-protein and RNA-ATAC datasets show that CHAMPOLLION outperforms existing approaches, remaining accurate with few paired cells and even generalizing to unseen cell types. Beyond alignment, CHAMPOLLION reveals biologically meaningful cross-modal relationships, highlighting in scRNA-protein data a potential role for CD18 across multiple cancers, and, in a human tonsil atlas combining scRNA-seq and scATAC-seq, suggesting that MEF2C may regulate inflammatory responses beyond the brain, notably in plasmacytoid dendritic cells.