# [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance]()

**Tong Chen**, **Yinuo Zhang**, **Pranam Chatterjee**

![AReUReDi_01](https://cdn-uploads.huggingface.co/production/uploads/649ef40be56dc456b7a36649/NXO9KZCTSM6j5ZOhgu-tr.png)

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.


Check out our paper on the [arXiv](https://arxiv.org/abs/2510.00352)!

## Citation

If you find this repository helpful for your papers and research, please consider citing our paper:

```python
@article{chen2025areuredi,
  title={AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance},
  author={Tong Chen and Yinuo Zhang and Pranam Chatterjee},
  journal={arXiv preprint arXiv:2510.00352},
  year={2025}
}
```