DiMOS: Doob-Guided Inference-Time Multi-Objective Search for Scientific Design

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.

Offline multi-objective optimization (Offline MOO) seeks Pareto-optimal designs from static datasets without additional environment interactions. Existing generative methods typically guide sampling with external surrogate or preference models, which adds training complexity and may provide unreliable guidance. We propose ParetoPilot, a plug-and-play method that guides designs to Pareto front at inference time using a pre-trained conditional diffusion model without any surrogate. ParetoPilot introduces an Infer-Perturb-Guide (IPG) engine within the reverse diffusion process. IPG first infers the individual conditional target for each sample in the batch by aligning its conditional and unconditional predictions. It then perturbs these targets collectively across the batch, balancing convergence toward the Pareto front and diversity among samples. Finally, the engine guides the generative trajectory toward the Pareto front by injecting these perturbed targets via standard Classifier-Free Guidance (CFG). Experiments on 51 tasks demonstrate that ParetoPilot achieves the best overall ranking among 16 methods and competitive hypervolume improvement.

Scientific discovery often involves optimising expensive-to-evaluate objectives over vast, structured, and open-ended hypothesis spaces, such as molecules, protein sequences, and computer programs. Generative models such as large language models (LLMs) provide expressive priors over such spaces, but their likelihoods and self-assessments are unreliable proxies for the objectives and calibrated epistemic uncertainty, especially for novel candidates outside the observed data distribution. We introduce the Large Discovery Model (LDM), an empirically grounded recurrent architecture that couples a generative model with a Bayesian non-parametric reward surrogate model. The generative model proposes and refines candidate designs, while the surrogate predicts their performance and quantifies uncertainty, yielding an uncertainty-aware value that guides candidate generation, refinement, and selection. The discovery memory and the surrogate model are continually updated as each new experimental observation arrives. We evaluate LDM on three scenarios spanning different design modalities and objectives, including neural-network training, antibody design, and molecular optimisation. Compared to LLM-only reflection or traditional statistical search across these domains, LDM achieves a $2.4\times$ greater reduction in validation BPB, an $18.2\%$ relative decrease in binding energy, and more than $60\%$ relative gains in molecular multi-objective performance. These results suggests that LDM could serve as a general-purpose discovery engine for effective search over open-ended hypothesis spaces.