Steering Where to Diffuse: Generative Modeling of Phenotypic Response Simulation with Steered Diffusion Bridge

Simulation of cellular morphology change has long been a fundamental task in quantitative biology and highthroughput screening, with the potential to accelerate therapeutic development and elucidate disease mechanisms beyond empirical clinical practice. However, the vast perturbation space poses challenges to the discriminative formulation, and existing generative approaches tend to concentrate on the same trajectory subspace, making their generated paths prone to drift. In this paper, we propose a novel Steered Diffusion Bridge approach, named SimuSDB, to define deterministic probabilistic trajectories between two distinct state domains for cell response generation. We first extend the diffusion bridge paradigm to maintain stochasticity and diversity in interpolation trajectories by introducing Brownian bridges. Then, SimuSDB generates cell morphologies that comply with phenotypic constraints, while allowing the latter to explicitly guide the generative process. For the inference stage, we formalize the ruleguided sample generation task as an optimal control problem within a stochastic dynamical system. This way, the generative model can achieve analytically tractable optimal control strategies and steered generation without collapsing toward the trajectory of the same data subspace. Comprehensive experiments demonstrate the superior performance of SimuSDB across various applications, including chemical perturbation and genetic perturbation.