Constructive CytoBridge: Simulation-Free Stochastic Control of Interacting Particles

Learning continuous cell-state dynamics from unpaired single-cell snapshots is essential for understanding cellular transitions and interactions. Achieving this without trajectory simulation becomes particularly challenging in the presence of pairwise cell–cell interactions, because they couple endpoint matching with the conditional paths connecting matched cells. Here we introduce Constructive CytoBridge (CCB), a simulation-free framework for stochastic optimal control with prescribed external and pairwise potentials. By conditioning on endpoint pairs and decomposing the control cost, CCB reveals an entropy-regularized quadratic OT structure in stochastic optimal control problems with pairwise interactions. We solve the resulting coupled problem by alternating KL-proximal transport updates with optimization of neural-network-parameterized conditional paths, and then regress a velocity field and a score function to support both deterministic and stochastic inference without requiring trajectory simulation during training. Experiments on synthetic and real datasets show that CCB accurately recovers the optimal control law and reconstructs marginal distributions, while incorporating external and pairwise potentials improves interpolation at unobserved time points.