COMPOSE: Molecular Generation and Optimization with a Reusable Stochastic Rewrite Process

Controllable molecular design requires models that describe how molecules can change and steer those changes toward desired outcomes. Existing models often specialize in particular endpoint distributions or task objectives, limiting their reuse as design goals change. To address this, we introduce **COMPOSE** (**CO**ntrollable **M**olecular **P**rocess **O**ver **S**tochastic **E**dits), which generates molecules through stochastic sequences of executable transformations between complete, chemically valid structures. We learn a goal-independent reference process over legal, variable-size transitions defined by an exact rewrite system. Structured programs combine these transitions into coordinated molecular transformations, while a separate controller steers them using task constraints and feedback. Keeping this reference process fixed, COMPOSE maintained 100% validity and achieved the highest mean quality among the compared methods across fragment-constrained generation tasks. This reuse extended to black-box optimization, where COMPOSE achieved a mean final top-10 score of 0.563 across 22 objectives, exceeding the strongest compared baseline's 0.542 under a 1,000-evaluation budget. In protein-specific lead optimization, COMPOSE obtained the best reported docking scores in 23 of 30 cases using 250 evaluations per lead, compared with 1,000 for the baselines. Together with similarity-constrained editing results, these findings show that reusable molecular transformations enable a single learned process to support generation and optimization as structural constraints and design objectives change, without retraining the underlying model.