DRIFT: Directed Developmental Geometry for Spatiotemporal Transcriptomic Alignment

Aligning unpaired spatial transcriptomic snapshots across developmental time is essential for reconstructing tissue dynamics, yet existing approaches primarily rely on transcriptomic similarity and spatial organization, which may yield developmentally implausible correspondences. We introduce DRIFT, a framework that incorporates directed developmental geometry into spatiotemporal transcriptomic alignment. DRIFT infers cell-type developmental reachability from velocity-informed single-cell dynamics and lifts this geometry to heterogeneous spatial spots through composition-aware optimal transport. The resulting developmental distance is integrated with transcriptomic and spatial information in a unified transport objective for cross-time alignment. Across four human spatiotemporal transcriptomics datasets, DRIFT produces correspondences that are more consistent with reference lineage structures and exhibit lower developmental deviation than representative transport-based baselines. These improved alignments also support more accurate held-out stage reconstruction under both linear transport and flow matching, with strong performance in both interpolation and extrapolation settings. Our code is publicly available at [https://github.com/xxx/DRIFT](https://anonymous.4open.science/r/DRIFT-review-3F38/README.md).