aiqbench analysis
This research introduces Unbalanced Schrödinger Bridge (USB), a simulation-free framework that addresses the limitations of continuous fluid models in capturing discrete birth-death events at single-cell resolution. By providing a tractable solution to the Branching Schrödinger Bridge problem, the method effectively scales to high-dimensional omics data while maintaining performance comparable to deterministic baselines. The approach offers a rigorous microscopic interpretation essential for accurately modeling lineage branching and fate decisions in stochastic cellular environments.
Beyond Continuity: Simulation-free Reconstruction of Discrete Branching Dynamics from Single-cell Snapshots
arXiv:2605.00545v2 Announce Type: replace Abstract: Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods treat mass as a continuous fluid, performing inference at the population level. However, this macroscopic view often fails to capture the discrete, jump-like nature of birth-death events at single-cell resolution, which is essential for understanding lineage branching and fate decisions. We present Unbalanced Schr\"odinger Bridge (USB), a simulation-free framework for learning underlying dynamics that effectively integrates both stochastic and unbalanced effects which also models the discrete, jump-like birth-death dynamics at single-cell resolution. Theoretically, USB provides a tractable solution to the Branching Schr\"odinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps. Technically, the method implements an efficient solver by introducing a simulation-free training objective that effectively scales to high-dimensional omics data. Empirically, we demonstrate on both simulated and real-world datasets that USB not only achieves trajectory reconstruction performance better than or comparable to deterministic baselines but also uniquely enables realistic discrete simulation of birth-death dynamics at single-cell resolution.
Abstract:Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods treat mass as a continuous fluid, performing inference at the population level. However, this macroscopic view often fails to capture the discrete, jump-like nature of birth-death events at single-cell resolution, which is essential for understanding lineage branching and fate decisions. We present Unbalanced Schrödinger Bridge (USB), a simulation-free framework for learning underlying dynamics that effectively integrates both stochastic and unbalanced effects which also models the discrete, jump-like birth-death dynamics at single-cell resolution. Theoretically, USB provides a tractable solution to the Branching Schrödinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps. Technically, the method implements an efficient solver by introducing a simulation-free training objective that effectively scales to high-dimensional omics data. Empirically, we demonstrate on both simulated and real-world datasets that USB not only achieves trajectory reconstruction performance better than or comparable to deterministic baselines but also uniquely enables realistic discrete simulation of birth-death dynamics at single-cell resolution.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Mathematical Physics (math-ph); Genomics (q-bio.GN); Quantitative Methods (q-bio.QM)
arXiv:2605.00545 [cs.LG]
(or arXiv:2605.00545v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.00545 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 290 words
