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+# [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance]()
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+**Tong Chen**, **Yinuo Zhang**, **Pranam Chatterjee**
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+![AReUReDi_01](https://cdn-uploads.huggingface.co/production/uploads/649ef40be56dc456b7a36649/NXO9KZCTSM6j5ZOhgu-tr.png)
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+Designing sequences that satisfy multiple, often conflicting, objectives is a central challenge in therapeutic and biomolecular engineering. Existing generative frameworks largely operate in continuous spaces with single-objective guidance, while discrete approaches lack guarantees for multi-objective Pareto optimality. We introduce **AReUReDi** (**A**nnealed **Re**ctified **U**pdates for **Re**fining **Di**screte Flows), a discrete optimization algorithm with theoretical guarantees of convergence to the Pareto front. Building on Rectified Discrete Flows (ReDi), AReUReDi combines Tchebycheff scalarization, locally balanced proposals, and annealed Metropolis-Hastings updates to bias sampling toward Pareto-optimal states while preserving distributional invariance. Applied to peptide and SMILES sequence design, AReUReDi simultaneously optimizes up to five therapeutic properties (including affinity, solubility, hemolysis, half-life, and non-fouling) and outperforms both evolutionary and diffusion-based baselines. These results establish AReUReDi as a powerful, sequence-based framework for multi-property biomolecule generation.