# Diffusing on Two Levels and Optimizing for Multiple Properties: A Novel Approach to Generating Molecules with Desirable Properties

arXiv: https://arxiv.org/abs/2310.04463 · HTML: https://mlsanity.com/paper/2310.04463/

## Key facts

- Cited by 5 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 18 of its 42 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## 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, 18 of 18)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Objective-Reinforced Generative Adversarial Networks (ORGAN) for Sequence Generation Models](https://mlsanity.com/paper/1705.10843/) (2017)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [Hit and Lead Discovery with Explorative RL and Fragment-based Molecule Generation](https://mlsanity.com/paper/2110.01219/) (2021)
- [NeVAE: A Deep Generative Model for Molecular Graphs](https://mlsanity.com/paper/1802.05283/) (2018)

## Built on by (most cited first, 5 of 5)

- [Improving Molecule Generation and Drug Discovery with a Knowledge-enhanced Generative Model](https://mlsanity.com/paper/2402.08790/) (2024)
- [Molecular Generative Adversarial Network with Multi-Property Optimization](https://mlsanity.com/paper/2404.00081/) (2024)
- [M3-20M: A Large-Scale Multi-Modal Molecule Dataset for AI-driven Drug Design and Discovery](https://mlsanity.com/paper/2412.06847/) (2024)
- [Cross-Modality Controlled Molecule Generation with Diffusion Language Model](https://mlsanity.com/paper/2508.14748/) (2025)
- [A Systematic Evaluation of Molecule Generation Models for De Novo Drug Design: From Benchmarks to Practical Insights](https://mlsanity.com/paper/2609.10099/) (2026)

## Abstract (arXiv)

In the past decade, Artificial Intelligence driven drug design and discovery has been a hot research topic, where an important branch is molecule generation by generative models, from GAN-based models and VAE-based models to the latest diffusion-based models. However, most existing models pursue only the basic properties like validity and uniqueness of the generated molecules, a few go further to explicitly optimize one single important molecular property (e.g. QED or PlogP), which makes most generated molecules little usefulness in practice. In this paper, we present a novel approach to generating molecules with desirable properties, which expands the diffusion model framework with multiple innovative designs. The novelty is two-fold. On the one hand, considering that the structures of molecules are complex and diverse, and molecular properties are usually determined by some substructures (e.g. pharmacophores), we propose to perform diffusion on two structural levels: molecules and molecular fragments respectively, with which a mixed Gaussian distribution is obtained for the reverse diffusion process. To get desirable molecular fragments, we develop a novel electronic effect based fragmentation method. On the other hand, we introduce two ways to explicitly optimize multiple molecular properties under the diffusion model framework. First, as potential drug molecules must be chemically valid, we optimize molecular validity by an energy-guidance function. Second, since potential drug molecules should be desirable in various properties, we employ a multi-objective mechanism to optimize multiple molecular properties simultaneously. Extensive experiments with two benchmark datasets QM9 and ZINC250k show that the molecules generated by our proposed method have better validity, uniqueness, novelty, Fr'echet ChemNet Distance (FCD), QED, and PlogP than those generated by current SOTA models.