PerturbBridge: Reference-Process Design for Heterogeneity-Aware Single-Cell Perturbation Prediction

Predicting single-cell perturbation responses requires transferring a known perturbation to new cellular contexts, where control and perturbed populations are measured separately and remain unpaired. Coupling-based prediction faces two connected challenges. First, standard transport costs can let heterogeneous response amplitudes dominate state correspondence. Second, endpoint optimal transport provides a static coupling but no process over intermediate states, so the coupling alone cannot ensure consistency with the paths required for training and generation. Changing the coupling cost while retaining a fixed bridge further separates the pairing geometry from the reference process used for training and generation. We therefore recast the problem as designing a reference process that jointly defines the coupling and supplies the intermediate states. We propose PerturbBridge, a heterogeneity-aware count reference whose two-parameter negative-binomial-difference family separates displacement scale from tail shape at fixed variance. Each member of the family induces a Schrödinger endpoint coupling and supplies its matching tractable integer bridge, so that coupling and generation remain reference-consistent as the geometry changes. Theoretically, we analyze two baseline states with different response amplitudes and establish conditions under which the reference preserves state correspondence regardless of response magnitude, and we connect this pairing preference to prediction error under composition shift. Empirically, PerturbBridge achieves strong overall rankings across 80 metrics spanning four expression views, ranking first among six learned models in all three PBMC settings. These results establish reference-process design as a principled approach to unpaired perturbation prediction under heterogeneous response amplitudes.