Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design

Goal-directed optimization is essential for steering molecular generators to propose candidates with desired properties. However, it is often implemented with policy-gradient reinforcement learning, which requires a generation-trajectory log-probability whose form depends on the model architecture and generation procedure. This makes an optimizer difficult to reuse across architectures and conditional generative designs. Supervised fine-tuning needs none of that machinery, but its update is driven by a fixed dataset, so the reward never enters the update. We introduce Elite-Weighted Supervised Fine-tuning (EW-SFT), which uses reward to guide elite selection of high-scoring molecules, and updates the model by its own pretraining loss on that set. Ablations show that reward information is passed primarily through elite selection, rather than through continuous weighting within the selected set. Because the update consumes only scored molecules and the model's native loss, the same rule applies across autoregressive, masked-diffusion, and discrete-flow generators, and across de novo, motif-extension, and linker-design tasks. Under a fixed budget of 3D shape alignment oracle calls on two kinase reference compounds, EW-SFT consistently outperforms the corresponding native optimizers. It further improves goal-directed optimization under a 2D similarity oracle on four held-out references and achieves comparable performance on a sample-efficiency benchmark without a trajectory-level RL formulation. These results demonstrate that EW-SFT is a unified and effective optimizer across molecular generators, design constraints, references, and oracles.

Despite the success of foundation models in language and vision, molecular graph generation still lacks a unified framework for heterogeneous design tasks with reliable controllability. While reinforcement learning (RL) offers a natural post-training mechanism for task-specific optimization, applying it to graph generative models is hindered by the vast atom-wise action spaces and chemically invalid intermediate states. We propose \textbf{Co}ntrollable \textbf{Mole}cular Generative Foundation Models (CoMole), built with a unified motif-aware graph diffusion pipeline. By learning a motif-aware graph space, CoMole transfers pretrained structural priors into controllable generation, where RL optimizes conditional reverse policies over chemically meaningful decisions. We theoretically characterize the bottleneck of atom-level RL and justify motif-aware policy optimization. Across three heterogeneous benchmarks spanning materials and drug discovery, CoMole ranks first in controllability on all nine targets, reduces MAE by up to 48.2% relative to the strongest baselines, and maintains validity above 0.94 without rule-based correction or post-hoc filtering. We further show that CoMole transfers controllability to unseen properties by optimizing only task embeddings with the generator frozen, achieving performance competitive with strong task-specific baselines.

Molecular optimization often starts from a pretrained generative model that captures a broad prior over valid molecular structures. At test time, however, the goal is not to sample from this prior, but to use a limited oracle budget to shift generation toward task-specific high-reward molecules. We study this adaptation problem for discrete diffusion models. Each online round couples several choices. The loop must decide which candidates to evaluate, how rewards become model updates, which feedback to reuse, and how far to move beyond the pretrained prior. These choices have mostly been studied in isolation, leaving open whether they complement one another, become redundant, or interfere inside a full online adaptation loop. We conduct controlled studies across six small-molecule binding-affinity tasks and three protein-fitness tasks. We find that acquisition, reward shaping, and model debiasing provide complementary routes to higher reward, especially for small molecules. Replay further stabilizes learning, while validity penalties keep small-molecule exploration on the valid molecular manifold. Together, these findings point to a practical recipe for feedback-efficient molecular optimization: online fine-tuning with acquisition, reward shaping, debiasing, replay, and validity control. This recipe outperforms offline fine-tuning and inference-time search baselines under matched oracle-call budgets and GPU-hour accounting. The gains are largest when high-reward candidates require larger shifts from the pretrained prior.