Uncertainty Aware Quality-Diversity Optimization For Offline Biological Sequence Design

Designing functional biological sequences requires navigating vast discrete spaces under strict evolutionary and biophysical constraints. Discrete Flow Matching (DFM) offers a generative framework over such spaces, but existing approaches rely on biologically uninformative couplings and offer limited flexibility for variable-length sequence generation and fine-grained control. We propose a structured coupling that encodes domain-specific preferences among sequence elements, biasing the source distribution toward plausible regions without modifying the flow objective or training procedure. Building on this, we introduce a latent edit-based rate parameterization that models variable-length generation via edit operations conditioned on a shared global latent, akin to a latent variable model, while remaining tractable. We further introduce a latent classifier-free guidance mechanism that steers generation coherently in continuous latent space, along with Dirichlet-prior temperature scaling for test-time control over edit operations. Our method achieves state-of-the-art performance across diverse biological sequence tasks, including density estimation, unconditional and conditional DNA sequence generation, and peptide sequence generation.

Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $\text{IGD}_\text{offline}$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.

Designing novel proteins with desired characteristics remains a significant challenge due to the large sequence space and the complexity of sequence-function relationships. Efficient exploration of this space to identify sequences that meet specific design criteria is crucial for advancing therapeutics and biotechnology. Here, we present BoGA (Bayesian Optimization Genetic Algorithm), a framework that combines evolutionary search with Bayesian optimization to efficiently navigate the sequence space. By integrating a genetic algorithm as a stochastic proposal generator within a surrogate modeling loop, BoGA prioritizes candidates based on prior evaluations and surrogate model predictions, enabling data-efficient optimization. We demonstrate the utility of BoGA through benchmarking on sequence and structure design tasks, followed by its application in designing peptide binders against pneumolysin, a key virulence factor of Streptococcus pneumoniae. BoGA accelerates the discovery of high-confidence binders, demonstrating the potential for efficient protein design across diverse objectives. The algorithm is implemented within the BoPep suite and is available under an MIT license at GitHub.