Property-Guided Molecular Generation and Optimization via Latent Flows

Adapting generative foundation models, in particular diffusion and flow models, to optimize given reward functions (e.g., binding affinity) while satisfying constraints (e.g., molecular synthesizability) is fundamental for their adoption in real-world scientific discovery applications such as molecular design or protein engineering. While recent works have introduced scalable methods for reward-guided fine-tuning of such models via reinforcement learning and control schemes, it remains an open problem how to algorithmically trade-off reward maximization and constraint satisfaction in a reliable and predictable manner. Motivated by this challenge, we first present a rigorous framework for Constrained Generative Optimization, which brings an optimization viewpoint to the introduced adaptation problem and retrieves the relevant task of constrained generation as a sub-case. Then, we introduce Constrained Flow Optimization (CFO), an algorithm that automatically and provably balances reward maximization and constraint satisfaction by reducing the original problem to sequential fine-tuning via established, scalable methods. We provide convergence guarantees for constrained generative optimization and constrained generation via CFO. Ultimately, we present an experimental evaluation of CFO on both synthetic, yet illustrative, settings, and a molecular design task. Across these evaluations, CFO achieves consistent increases in reward while ensuring high constraint satisfaction, showcasing its practical utility for constrained generative optimization.

Modern graph generative models typically operate directly in the discrete graph space, explicitly generating node and edge variables, which can become costly as graphs grow. In this paper, we perform generation explicitly on latent representations of entire graphs obtained from a pretrained Variational Autoencoder with high reconstruction fidelity. The generated representations, obtained through flow matching, are then decoded only at the final step. Across molecular benchmarks of increasing size, our approach achieves strong validity and FCD while offering a favorable quality-efficiency trade-off compared with state-of-the-art explicit graph generative models. One of the main advantages of this formulation is that the graph representation only needs to be learned once, after which the same one can be reused across multiple generative objectives without retraining. We demonstrate generation guided by molecular properties and further introduce validity-aware generation though a classifier learned directly in latent space. All code will be made available upon acceptance.

Designing polymers with targeted properties requires navigating vast chemical spaces from limited labeled data. Here we introduce PolyLatentFlow, a framework based on continuous-time flow matching in latent space for unconditional and conditional polymer generation, together with LlamaUni, a multimodal representation combining polymer sequence and 3D structural information. In unconditional generation, PolyLatentFlow with LlamaUni produced the largest yield of valid candidates novel relative to PolyInfo among the evaluated unconditional generators while maintaining high diversity. For $T_g$ conditioning, generated property distributions shifted systematically across a 200 °C target range. In multi-property tasks, molecular representations showed similar surrogate target fidelity but differed markedly in validity, training-set replay, and structural proximity to labeled polymers. PolyLatentFlow with LlamaUni consistently combined high validity with low replay and achieved the largest per-attempt yield of nonreplayed target hits for CO$_2$/N$_2$ conditioning. These results demonstrate latent space flow matching for polymer inverse design and identify molecular representation as a key determinant of target control and exploration beyond labeled chemistry.