# pCoMole: Pareto-Constrained Molecule Editing with Discrete Flows

arXiv: https://arxiv.org/abs/2610.01663 · HTML: https://mlsanity.com/paper/2610.01663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 79 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 25 of 25)

- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [ChemBERTa: Large-Scale Self-Supervised Pretraining for Molecular Property Prediction](https://mlsanity.com/paper/2010.09885/) (2020)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Molecular De Novo Design through Deep Reinforcement Learning](https://mlsanity.com/paper/1704.07555/) (2017)
- [Optimization of Molecules via Deep Reinforcement Learning](https://mlsanity.com/paper/1810.08678/) (2018)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusion](https://mlsanity.com/paper/2412.17780/) (2024)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Constrained Discrete Diffusion](https://mlsanity.com/paper/2503.09790/) (2025)
- [Multi-Objective-Guided Discrete Flow Matching for Controllable Biological Sequence Design](https://mlsanity.com/paper/2505.07086/) (2025)
- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2110.06980/) (2021)
- [Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2406.08799/) (2024)
- [A Diffusion Model to Shrink Proteins While Maintaining Their Function](https://mlsanity.com/paper/2511.07390/) (2025)
- [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance](https://mlsanity.com/paper/2510.00352/) (2025)
- [Multi-Constrained Evolutionary Molecular Design Framework: An Interpretable Drug Design Method Combining Rule-Based Evolution and Molecular Crossover](https://mlsanity.com/paper/2601.10110/) (2026)

## Abstract (arXiv)

Biomolecular therapeutics often start from known sequences and require targeted editing to improve multiple properties while satisfying hard biochemical and manufacturability constraints. However, existing generative methods do not jointly support multi-objective optimization, hard feasibility, and sequence editing in discrete, variable-length biological spaces. In this work, we introduce Pareto-Constrained Molecule Editing (pCoMole), a framework built on discrete flow matching that steers a pre-trained Edit Flow toward user-specified preferences while enforcing terminal feasibility. pCoMole defines a feasibility-gated terminal distribution using an augmented Tchebycheff utility and realizes the resulting preference tilt through a Doob-h transform of the underlying edit process. To make this construction practical, we approximate the required harmonic function using short Monte Carlo rollouts over candidate edits, yielding an efficient guided editor with provable preference consistency. We validate pCoMole by shrinking GFP while retaining fluorescence-related properties, shortening diverse Cas9 orthologs while preserving PAM specificity, and compressing peptide binders into short peptidomimetics that optimize seven drug-related properties under hard constraints. In wet lab testing, two 229-residue pCoMole-designed eGFP variants retained clear green fluorescence in BL21 cells after 10 deletions, with either one or two substitutions. Together, pCoMole enables constraint-aware, Pareto-aligned editing of biomolecular sequences in discrete, variable-length spaces.