# Sample-efficient Multi-objective Molecular Optimization with GFlowNets

arXiv: https://arxiv.org/abs/2302.04040 · HTML: https://mlsanity.com/paper/2302.04040/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 67 references that are in the map.
- First posted on arXiv 8 Feb 2023.

## Builds on (most cited first, 30 of 40)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Neural Architecture Search with Bayesian Optimisation and Optimal Transport](https://mlsanity.com/paper/1802.07191/) (2018)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Sample Efficiency Matters: A Benchmark for Practical Molecular Optimization](https://mlsanity.com/paper/2206.12411/) (2022)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)

## Built on by (most cited first, 30 of 50)

- [Panacea: Pareto Alignment via Preference Adaptation for LLMs](https://mlsanity.com/paper/2402.02030/) (2024)
- [Efficient Evolutionary Search Over Chemical Space with Large Language Models](https://mlsanity.com/paper/2406.16976/) (2024)
- [Ant Colony Sampling with GFlowNets for Combinatorial Optimization](https://mlsanity.com/paper/2403.07041/) (2024)
- [Improved off-policy training of diffusion samplers](https://mlsanity.com/paper/2402.05098/) (2024)
- [Graph Diffusion Transformers for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2401.13858/) (2024)
- [Genetic-guided GFlowNets for Sample Efficient Molecular Optimization](https://mlsanity.com/paper/2402.05961/) (2024)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [ParetoFlow: Guided Flows in Multi-Objective Optimization](https://mlsanity.com/paper/2412.03718/) (2024)
- [Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization](https://mlsanity.com/paper/2405.19650/) (2024)
- [Pessimistic Backward Policy for GFlowNets](https://mlsanity.com/paper/2405.16012/) (2024)
- [Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximization](https://mlsanity.com/paper/2410.15474/) (2024)
- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [Beyond Squared Error: Exploring Loss Design for Enhanced Training of Generative Flow Networks](https://mlsanity.com/paper/2410.02596/) (2024)
- [FERERO: A Flexible Framework for Preference-Guided Multi-Objective Learning](https://mlsanity.com/paper/2412.01773/) (2024)
- [Molecule Design by Latent Prompt Transformer](https://mlsanity.com/paper/2310.03253/) (2023)
- [Generative AI for Controllable Protein Sequence Design: A Survey](https://mlsanity.com/paper/2402.10516/) (2024)
- [Learning Flexible Forward Trajectories for Masked Molecular Diffusion](https://mlsanity.com/paper/2505.16790/) (2025)
- [Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2510.04792/) (2025)
- [MolHF: A Hierarchical Normalizing Flow for Molecular Graph Generation](https://mlsanity.com/paper/2305.08457/) (2023)
- [Reference-guided Policy Optimization for Molecular Optimization via LLM Reasoning](https://mlsanity.com/paper/2603.05900/) (2026)
- [GFlowNet Pretraining with Inexpensive Rewards](https://mlsanity.com/paper/2409.09702/) (2024)
- [Graph-structured Small Molecule Drug Discovery Through Deep Learning: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2502.08975/) (2025)
- [Pretraining Generative Flow Networks with Inexpensive Rewards for Molecular Graph Generation](https://mlsanity.com/paper/2503.06337/) (2025)
- [ToolMol: Evolutionary Agentic Framework for Multi-objective Drug Discovery](https://mlsanity.com/paper/2605.12784/) (2026)
- [Preference-Optimized Pareto Set Learning for Blackbox Optimization](https://mlsanity.com/paper/2408.09976/) (2024)
- [InversionGNN: A Dual Path Network for Multi-Property Molecular Optimization](https://mlsanity.com/paper/2503.01488/) (2025)
- [Curriculum-Augmented GFlowNets For mRNA Sequence Generation](https://mlsanity.com/paper/2510.03811/) (2025)
- [LLM-Guided Dynamic Action Spaces for Synthesizable Molecular Optimization](https://mlsanity.com/paper/2604.07669/) (2026)
- [Molecular Lead Optimization via Agentic Tool Planning](https://mlsanity.com/paper/2605.28862/) (2026)
- [MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning](https://mlsanity.com/paper/2410.11226/) (2024)

## Abstract (arXiv)

Many crucial scientific problems involve designing novel molecules with desired properties, which can be formulated as a black-box optimization problem over the discrete chemical space. In practice, multiple conflicting objectives and costly evaluations (e.g., wet-lab experiments) make the diversity of candidates paramount. Computational methods have achieved initial success but still struggle with considering diversity in both objective and search space. To fill this gap, we propose a multi-objective Bayesian optimization (MOBO) algorithm leveraging the hypernetwork-based GFlowNets (HN-GFN) as an acquisition function optimizer, with the purpose of sampling a diverse batch of candidate molecular graphs from an approximate Pareto front. Using a single preference-conditioned hypernetwork, HN-GFN learns to explore various trade-offs between objectives. We further propose a hindsight-like off-policy strategy to share high-performing molecules among different preferences in order to speed up learning for HN-GFN. We empirically illustrate that HN-GFN has adequate capacity to generalize over preferences. Moreover, experiments in various real-world MOBO settings demonstrate that our framework predominantly outperforms existing methods in terms of candidate quality and sample efficiency. The code is available at https://github.com/violet-sto/HN-GFN.