Identifiable Feedback-Controlled Latent Flow for Unpaired Single-cell Spatio-Temporal Dynamics

Reconstructing the gene regulatory dynamics underlying tissue development from unpaired, cross-sectional spatial transcriptomic snapshots poses a significant challenge in single-cell biology. While recent optimal transport and flow-based methods have advanced trajectory interpolation, their unconstrained latent dynamics lack identifiability, hindering reliable discovery of the underlying regulatory mechanisms. To address this, we propose single-cell Identifiable Feedback-controlled Latent Flow (scIFLF), a generative framework that introduces a physics-inspired structural prior that decomposes the latent flow into a macroscopic developmental drift and a restorative feedback toward functional attractors. Crucially, the gene-regulatory Jacobian is shown to be uniquely identifiable, invariant to the latent ambiguity, enabling principled discovery of gene regulations directly from the learned flow. Implemented with a multimodal Neural ODE, scIFLF aligns latent trajectories using entropy-regularized optimal transport. Benchmark experiments demonstrate that scIFLF outperforms state-of-the-art methods in trajectory interpolation and spatial coherence, while successfully recovering key driver genes of tissue development and organogenesis, bridging the gap between deep generative flexibility and biological interpretability.