# Routing by Reaching: Composition of Pre-trained GFlowNets for Multi-Objective Generation

arXiv: https://arxiv.org/abs/2602.21565 · HTML: https://mlsanity.com/paper/2602.21565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 29 of 29)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [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)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [A Literature Survey of Benchmark Functions For Global Optimization Problems](https://mlsanity.com/paper/1308.4008/) (2013)
- [Unsupervised Learning of Compositional Energy Concepts](https://mlsanity.com/paper/2111.03042/) (2021)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space](https://mlsanity.com/paper/2404.12141/) (2024)
- [Molecular Mechanics-Driven Graph Neural Network with Multiplex Graph for Molecular Structures](https://mlsanity.com/paper/2011.07457/) (2020)
- [PoET: A generative model of protein families as sequences-of-sequences](https://mlsanity.com/paper/2306.06156/) (2023)
- [Compositional Sculpting of Iterative Generative Processes](https://mlsanity.com/paper/2309.16115/) (2023)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)
- [Order-Preserving GFlowNets](https://mlsanity.com/paper/2310.00386/) (2023)

## Abstract (arXiv)

Generative Flow Networks (GFlowNets) learn to sample diverse candidates in proportion to a reward function, making them well-suited for scientific discovery, where exploring multiple promising solutions is crucial. Further extending GFlowNets to multi-objective settings has attracted growing interest as real-world applications often involve multiple, conflicting objectives. However, existing approaches require joint training for each combination of objectives, meaning that any change in the objective set necessitates retraining from scratch. We propose a framework that composes pre-trained GFlowNets at inference time, enabling rapid adaptation without fine-tuning or retraining. Importantly, our framework is flexible, capable of handling diverse reward combinations ranging from linear scalarization to complex nonlinear operators, which are often handled separately in previous literature. We prove that our method exactly recovers the target distribution for linear scalarization, and quantify the approximation quality for nonlinear operators through a distortion factor. Experiments on a synthetic 2D grid and real-world molecule generation tasks demonstrate that our approach achieves performance comparable to baselines.