Beyond Continuity: Simulation-free Reconstruction of Discrete Branching Dynamics from Single-cell Snapshots

2026-05-01

AI Summary

This work addresses the challenge of simultaneously modeling non-conserved mass dynamics—such as cell proliferation and apoptosis—and discrete birth-death events in single-cell trajectory inference. To this end, the authors propose the Unbalanced Schrödinger Bridge (USB) framework, which extends the branched Schrödinger bridge problem to unbalanced settings involving discrete jumps, enabling joint modeling of cellular Brownian motion and birth-death dynamics without requiring explicit simulation. Grounded in unbalanced optimal transport theory, USB introduces a simulation-free training objective and develops an efficient solver tailored for high-dimensional omics data. Experiments demonstrate that USB matches or outperforms existing deterministic methods on both synthetic and real datasets, offering the first approach capable of faithfully modeling discrete birth-death processes 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.

Problem

• single-cell
• branching dynamics
• birth-death processes
• unbalanced optimal transport
• trajectory inference

Innovation

• Unbalanced Schrödinger Bridge
• single-cell trajectory inference
• discrete birth-death dynamics
• simulation-free learning
• branching dynamics