# Multi-Objective GFlowNets

arXiv: https://arxiv.org/abs/2210.12765 · HTML: https://mlsanity.com/paper/2210.12765/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 80 references that are in the map.
- First posted on arXiv 23 Oct 2022.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [A Survey of Multi-Objective Sequential Decision-Making](https://mlsanity.com/paper/1402.0590/) (2014)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation](https://mlsanity.com/paper/1908.08342/) (2019)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Generalized Denoising Auto-Encoders as Generative Models](https://mlsanity.com/paper/1305.6663/) (2013)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [A Distributional View on Multi-Objective Policy Optimization](https://mlsanity.com/paper/2005.07513/) (2020)
- [Molecular Mechanics-Driven Graph Neural Network with Multiplex Graph for Molecular Structures](https://mlsanity.com/paper/2011.07457/) (2020)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [Pareto Conditioned Networks](https://mlsanity.com/paper/2204.05036/) (2022)
- [Conditioning Sparse Variational Gaussian Processes for Online Decision-making](https://mlsanity.com/paper/2110.15172/) (2021)

## Built on by (most cited first, 30 of 101)

- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Panacea: Pareto Alignment via Preference Adaptation for LLMs](https://mlsanity.com/paper/2402.02030/) (2024)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (2023)
- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [Local Search GFlowNets](https://mlsanity.com/paper/2310.02710/) (2023)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [GFlowNet-EM for learning compositional latent variable models](https://mlsanity.com/paper/2302.06576/) (2023)
- [Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets](https://mlsanity.com/paper/2305.17010/) (2023)
- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (2025)
- [Stochastic Generative Flow Networks](https://mlsanity.com/paper/2302.09465/) (2023)
- [Thompson sampling for improved exploration in GFlowNets](https://mlsanity.com/paper/2306.17693/) (2023)
- [Maximum entropy GFlowNets with soft Q-learning](https://mlsanity.com/paper/2312.14331/) (2023)
- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [Compositional Sculpting of Iterative Generative Processes](https://mlsanity.com/paper/2309.16115/) (2023)
- [Learning to Scale Logits for Temperature-Conditional GFlowNets](https://mlsanity.com/paper/2310.02823/) (2023)
- [Improving GFlowNets for Text-to-Image Diffusion Alignment](https://mlsanity.com/paper/2406.00633/) (2024)
- [SynFlowNet: Design of Diverse and Novel Molecules with Synthesis Constraints](https://mlsanity.com/paper/2405.01155/) (2024)
- [MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation](https://mlsanity.com/paper/2406.07529/) (2024)
- [Generative Flows on Synthetic Pathway for Drug Design](https://mlsanity.com/paper/2410.04542/) (2024)
- [Pareto Set Learning for Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2501.06773/) (2025)
- [QGFN: Controllable Greediness with Action Values](https://mlsanity.com/paper/2402.05234/) (2024)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Goal-conditioned GFlowNets for Controllable Multi-Objective Molecular Design](https://mlsanity.com/paper/2306.04620/) (2023)
- [Pre-Training and Fine-Tuning Generative Flow Networks](https://mlsanity.com/paper/2310.03419/) (2023)
- [ParetoFlow: Guided Flows in Multi-Objective Optimization](https://mlsanity.com/paper/2412.03718/) (2024)
- [DiverseFlow: Sample-Efficient Diverse Mode Coverage in Flows](https://mlsanity.com/paper/2504.07894/) (2025)
- [Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization](https://mlsanity.com/paper/2405.19650/) (2024)

## Abstract (arXiv)

We study the problem of generating diverse candidates in the context of Multi-Objective Optimization. In many applications of machine learning such as drug discovery and material design, the goal is to generate candidates which simultaneously optimize a set of potentially conflicting objectives. Moreover, these objectives are often imperfect evaluations of some underlying property of interest, making it important to generate diverse candidates to have multiple options for expensive downstream evaluations. We propose Multi-Objective GFlowNets (MOGFNs), a novel method for generating diverse Pareto optimal solutions, based on GFlowNets. We introduce two variants of MOGFNs: MOGFN-PC, which models a family of independent sub-problems defined by a scalarization function, with reward-conditional GFlowNets, and MOGFN-AL, which solves a sequence of sub-problems defined by an acquisition function in an active learning loop. Our experiments on wide variety of synthetic and benchmark tasks demonstrate advantages of the proposed methods in terms of the Pareto performance and importantly, improved candidate diversity, which is the main contribution of this work.