AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with
  Multi-Objective Guidance
Authors: name: Tong Chen, name: Yinuo Zhang, name: Pranam Chatterjee

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 (Annealed Rectified
Updates for Refining Discrete 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.