PACE: Geometry-Aware Bridge Transport for Single-Cell Trajectory Inference
Abstract
Single-cell trajectory inference from destructive time-course snapshots is fundamentally ill-posed: neither cross-time cell correspondences nor continuous trajectories are observed, so the snapshot distributions alone do not uniquely determine the underlying dynamics. Existing optimal transport and flow-based methods typically couple cells by Euclidean proximity at observed clock times, which can misalign trajectories when development is asynchronous and cells sampled at the same experimental time occupy different latent pseudotime stages. We propose PACE, a trajectory inference framework that recovers geometry-consistent continuous transport dynamics from destructive time-course snapshots through three coupled components. First, PACE constructs a state- and time-dependent anisotropic Riemannian metric that assigns low transport cost along locally supported tangent directions while penalizing normal velocity components. Second, it alternates between refining cross-time couplings under the induced path-action cost and fitting endpoint-preserving neural bridges between adjacent snapshots. Third, it distills the learned bridge dynamics into a global continuous-time velocity field over cellular states. Across seven controlled and biological datasets covering nine held-out reconstruction experiments, PACE achieves the strongest overall reconstruction performance, reducing MMD, Wasserstein-1 distance, and Wasserstein-2 distance by 23.7% on average relative to the strongest competing baseline. PACE also improves RNA-velocity alignment by 15.4% on an embryoid body differentiation benchmark, without requiring explicit cell pairing, lineage tracing, or RNA-velocity supervision during training. Code is available at https://github.com/AI4Science-WestlakeU/PACE.
Related
- BioTrajX: evaluating biological plausibility in single-cell trajectory inference
- CardamomOT: A mechanistic optimal transport-based framework for gene regulatory network inference, trajectory reconstruction and generative modeling
- Mechanistic gene-regulation-based trajectory inference with bowside
- Multi-Trajectory Pseudotime Inference via Permutation Factorizations
- Chapter 2: Geometry of the Fitness Surface and Trajectory Dynamics of Replicator Systems
BibTeX
@misc{yu2026pace,
title = {{PACE: Geometry-Aware Bridge Transport for Single-Cell Trajectory Inference}},
author = {Chenglei Yu and Chuanrui Wang and Bangyan Liao and Tailin Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.18587},
eprint = {2605.18587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.18587},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - PACE: Geometry-Aware Bridge Transport for Single-Cell Trajectory Inference
AU - Chenglei Yu
AU - Chuanrui Wang
AU - Bangyan Liao
AU - Tailin Wu
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2605.18587
UR - https://arxiv.org/abs/2605.18587
AB - Single-cell trajectory inference from destructive time-course snapshots is fundamentally ill-posed: neither cross-time cell correspondences nor continuous trajectories are observed, so the snapshot distributions alone do not uniquely determine the underlying dynamics. Existing optimal transport and flow-based methods typically couple cells by Euclidean proximity at observed clock times, which can misalign trajectories when development is asynchronous and cells sampled at the same experimental time occupy different latent pseudotime stages. We propose PACE, a trajectory inference framework that recovers geometry-consistent continuous transport dynamics from destructive time-course snapshots through three coupled components. First, PACE constructs a state- and time-dependent anisotropic Riemannian metric that assigns low transport cost along locally supported tangent directions while penalizing normal velocity components. Second, it alternates between refining cross-time couplings under the induced path-action cost and fitting endpoint-preserving neural bridges between adjacent snapshots. Third, it distills the learned bridge dynamics into a global continuous-time velocity field over cellular states. Across seven controlled and biological datasets covering nine held-out reconstruction experiments, PACE achieves the strongest overall reconstruction performance, reducing MMD, Wasserstein-1 distance, and Wasserstein-2 distance by 23.7% on average relative to the strongest competing baseline. PACE also improves RNA-velocity alignment by 15.4% on an embryoid body differentiation benchmark, without requiring explicit cell pairing, lineage tracing, or RNA-velocity supervision during training. Code is available at https://github.com/AI4Science-WestlakeU/PACE.
ER -