# Differentiable Scaffolding Tree for Molecular Optimization

arXiv: https://arxiv.org/abs/2109.10469 · HTML: https://mlsanity.com/paper/2109.10469/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 56 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [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)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [Optimization of Molecules via Deep Reinforcement Learning](https://mlsanity.com/paper/1810.08678/) (2018)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [Syntax-Directed Variational Autoencoder for Structured Data](https://mlsanity.com/paper/1802.08786/) (2018)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)
- [Learning Multimodal Graph-to-Graph Translation for Molecular Optimization](https://mlsanity.com/paper/1812.01070/) (2018)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendations](https://mlsanity.com/paper/1908.01425/) (2019)
- [The Synthesizability of Molecules Proposed by Generative Models](https://mlsanity.com/paper/2002.07007/) (2020)
- [Augmenting Genetic Algorithms with Deep Neural Networks for Exploring the Chemical Space](https://mlsanity.com/paper/1909.11655/) (2019)
- [Learning To Navigate The Synthetically Accessible Chemical Space Using Reinforcement Learning](https://mlsanity.com/paper/2004.12485/) (2020)
- [MIMOSA: Multi-constraint Molecule Sampling for Molecule Optimization](https://mlsanity.com/paper/2010.02318/) (2020)
- [CORE: Automatic Molecule Optimization Using Copy & Refine Strategy](https://mlsanity.com/paper/1912.05910/) (2019)
- [Graph Residual Flow for Molecular Graph Generation](https://mlsanity.com/paper/1909.13521/) (2019)
- [Improving the Similarity Measure of Determinantal Point Processes for Extractive Multi-Document Summarization](https://mlsanity.com/paper/1906.00072/) (2019)

## Built on by (most cited first, 30 of 53)

- [Machine Learning for Synthetic Data Generation: A Review](https://mlsanity.com/paper/2302.04062/) (2023)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Efficient Evolutionary Search Over Chemical Space with Large Language Models](https://mlsanity.com/paper/2406.16976/) (2024)
- [Multimodal learning with graphs](https://mlsanity.com/paper/2209.03299/) (2022)
- [Regression Transformer: Concurrent sequence regression and generation for molecular language modeling](https://mlsanity.com/paper/2202.01338/) (2022)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [Reinforced Genetic Algorithm for Structure-based Drug Design](https://mlsanity.com/paper/2211.16508/) (2022)
- [Graph Diffusion Transformers for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2401.13858/) (2024)
- [Amortized Tree Generation for Bottom-up Synthesis Planning and Synthesizable Molecular Design](https://mlsanity.com/paper/2110.06389/) (2021)
- [DrugAgent: Automating AI-aided Drug Discovery Programming through LLM Multi-Agent Collaboration](https://mlsanity.com/paper/2411.15692/) (2024)
- [LIMO: Latent Inceptionism for Targeted Molecule Generation](https://mlsanity.com/paper/2206.09010/) (2022)
- [State-specific protein-ligand complex structure prediction with a multi-scale deep generative model](https://mlsanity.com/paper/2209.15171/) (2022)
- [How Much Space Has Been Explored? Measuring the Chemical Space Covered by Databases and Machine-Generated Molecules](https://mlsanity.com/paper/2112.12542/) (2021)
- [TWIN-GPT: Digital Twins for Clinical Trials via Large Language Model](https://mlsanity.com/paper/2404.01273/) (2024)
- [Learning on Multimodal Graphs: A Survey](https://mlsanity.com/paper/2402.05322/) (2024)
- [Synthetic Data in AI: Challenges, Applications, and Ethical Implications](https://mlsanity.com/paper/2401.01629/) (2024)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [Uncertainty Quantification on Clinical Trial Outcome Prediction](https://mlsanity.com/paper/2401.03482/) (2024)
- [Generative Artificial Intelligence for Navigating Synthesizable Chemical Space](https://mlsanity.com/paper/2410.03494/) (2024)
- [Interpretable Molecular Graph Generation via Monotonic Constraints](https://mlsanity.com/paper/2203.00412/) (2022)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Molecule Generation for Drug Design: a Graph Learning Perspective](https://mlsanity.com/paper/2202.09212/) (2022)
- [A Review on Knowledge Graphs for Healthcare: Resources, Applications, and Promises](https://mlsanity.com/paper/2306.04802/) (2023)
- [Disentangled Spatiotemporal Graph Generative Models](https://mlsanity.com/paper/2203.00411/) (2022)
- [Deep Learning Methods for Small Molecule Drug Discovery: A Survey](https://mlsanity.com/paper/2303.00313/) (2023)
- [Molecule Design by Latent Space Energy-Based Modeling and Gradual Distribution Shifting](https://mlsanity.com/paper/2306.14902/) (2023)
- [Molecule Design by Latent Prompt Transformer](https://mlsanity.com/paper/2310.03253/) (2023)
- [3M-Diffusion: Latent Multi-Modal Diffusion for Language-Guided Molecular Structure Generation](https://mlsanity.com/paper/2403.07179/) (2024)
- [ExLLM: Experience-Enhanced LLM Optimization for Molecular Design and Beyond](https://mlsanity.com/paper/2502.12845/) (2025)

## Abstract (arXiv)

The structural design of functional molecules, also called molecular optimization, is an essential chemical science and engineering task with important applications, such as drug discovery. Deep generative models and combinatorial optimization methods achieve initial success but still struggle with directly modeling discrete chemical structures and often heavily rely on brute-force enumeration. The challenge comes from the discrete and non-differentiable nature of molecule structures. To address this, we propose differentiable scaffolding tree (DST) that utilizes a learned knowledge network to convert discrete chemical structures to locally differentiable ones. DST enables a gradient-based optimization on a chemical graph structure by back-propagating the derivatives from the target properties through a graph neural network (GNN). Our empirical studies show the gradient-based molecular optimizations are both effective and sample efficient. Furthermore, the learned graph parameters can also provide an explanation that helps domain experts understand the model output.