# Multi-Objective-Guided Discrete Flow Matching for Controllable Biological Sequence Design

arXiv: https://arxiv.org/abs/2505.07086 · HTML: https://mlsanity.com/paper/2505.07086/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 16 of its 52 references that are in the map.
- First posted on arXiv 11 May 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 16 of 16)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)
- [Fisher Flow Matching for Generative Modeling over Discrete Data](https://mlsanity.com/paper/2405.14664/) (2024)
- [PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusion](https://mlsanity.com/paper/2412.17780/) (2024)
- [PeptideBERT: A Language Model based on Transformers for Peptide Property Prediction](https://mlsanity.com/paper/2309.03099/) (2023)
- [ParetoFlow: Guided Flows in Multi-Objective Optimization](https://mlsanity.com/paper/2412.03718/) (2024)
- [Learning to design protein-protein interactions with enhanced generalization](https://mlsanity.com/paper/2310.18515/) (2023)
- [PROUD: PaRetO-gUided Diffusion Model for Multi-objective Generation](https://mlsanity.com/paper/2407.04493/) (2024)
- [Exploring Discrete Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2411.16644/) (2024)
- [Gumbel-Softmax Flow Matching with Straight-Through Guidance for Controllable Biological Sequence Generation](https://mlsanity.com/paper/2503.17361/) (2025)
- [A Continuous Relaxation for Discrete Bayesian Optimization](https://mlsanity.com/paper/2404.17452/) (2024)

## Built on by (most cited first, 15 of 15)

- [MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control](https://mlsanity.com/paper/2508.10684/) (2025)
- [Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimization](https://mlsanity.com/paper/2510.08233/) (2025)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [Steering Generative Models with Experimental Data for Protein Fitness Optimization](https://mlsanity.com/paper/2505.15093/) (2025)
- [Flow Matching for Offline Reinforcement Learning with Discrete Actions](https://mlsanity.com/paper/2602.06138/) (2026)
- [How to make the most of your masked language model for protein engineering](https://mlsanity.com/paper/2603.10302/) (2026)
- [TD3B: Transition-Directed Discrete Diffusion for Allosteric Binder Generation](https://mlsanity.com/paper/2605.09810/) (2026)
- [mRNAutilus: Multi-Objective-Guided Discrete Generation of mRNA with Optimized Therapeutic Properties](https://mlsanity.com/paper/2605.31296/) (2026)
- [Minimal-Action Discrete Schr"odinger Bridge Matching for Peptide Sequence Design](https://mlsanity.com/paper/2601.22408/) (2026)
- [A Time-Reparameterized Cumulative Intensity Extrapolation Sampler for Discrete Flow Matching](https://mlsanity.com/paper/2606.24140/) (2026)
- [Pepti-drift: Scalable Safe-Active Peptide Generation Without Inference-Time Guidance](https://mlsanity.com/paper/2606.27824/) (2026)
- [pCoMole: Pareto-Constrained Molecule Editing with Discrete Flows](https://mlsanity.com/paper/2610.01663/) (2026)
- [DiMOS: Doob-Guided Inference-Time Multi-Objective Search for Scientific Design](https://mlsanity.com/paper/2610.05808/) (2026)
- [LLM-to-Flow Distillation: Teaching Natural Language Goals to Scientific Generators](https://mlsanity.com/paper/2610.17246/) (2026)

## Abstract (arXiv)

Designing biological sequences that satisfy multiple, often conflicting, functional and biophysical criteria remains a central challenge in biomolecule engineering. While discrete flow matching models have recently shown promise for efficient sampling in high-dimensional sequence spaces, existing approaches address only single objectives or require continuous embeddings that can distort discrete distributions. We present Multi-Objective-Guided Discrete Flow Matching (MOG-DFM), a general framework to steer any pretrained discrete flow matching generator toward Pareto-efficient trade-offs across multiple scalar objectives. At each sampling step, MOG-DFM computes a hybrid rank-directional score for candidate transitions and applies an adaptive hypercone filter to enforce consistent multi-objective progression. We also trained two unconditional discrete flow matching models, PepDFM for diverse peptide generation and EnhancerDFM for functional enhancer DNA generation, as base generation models for MOG-DFM. We demonstrate MOG-DFM's effectiveness in generating peptide binders optimized across five properties (hemolysis, non-fouling, solubility, half-life, and binding affinity), and in designing DNA sequences with specific enhancer classes and DNA shapes. In total, MOG-DFM proves to be a powerful tool for multi-property-guided biomolecule sequence design.