# Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation

arXiv: https://arxiv.org/abs/2301.00427 · HTML: https://mlsanity.com/paper/2301.00427/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 54 references that are in the map.
- First posted on arXiv 1 Jan 2023.

## Builds on (most cited first, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [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)
- [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)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)

## Built on by (most cited first, 30 of 46)

- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Discrete Copula Diffusion](https://mlsanity.com/paper/2410.01949/) (2024)
- [Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization](https://mlsanity.com/paper/2402.08095/) (2024)
- [Learning Joint 2D & 3D Diffusion Models for Complete Molecule Generation](https://mlsanity.com/paper/2305.12347/) (2023)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Generative Modelling of Structurally Constrained Graphs](https://mlsanity.com/paper/2406.17341/) (2024)
- [NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generation](https://mlsanity.com/paper/2502.12638/) (2025)
- [A Survey of Graph Transformers: Architectures, Theories and Applications](https://mlsanity.com/paper/2502.16533/) (2025)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Advancing Graph Generation through Beta Diffusion](https://mlsanity.com/paper/2406.09357/) (2024)
- [ReDi: Efficient Learning-Free Diffusion Inference via Trajectory Retrieval](https://mlsanity.com/paper/2302.02285/) (2023)
- [Improving Classifier-Free Guidance in Masked Diffusion: Low-Dim Theoretical Insights with High-Dim Impact](https://mlsanity.com/paper/2507.08965/) (2025)
- [D4Explainer: In-Distribution GNN Explanations via Discrete Denoising Diffusion](https://mlsanity.com/paper/2310.19321/) (2023)
- [DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector](https://mlsanity.com/paper/2410.06549/) (2024)
- [What Exactly Does Guidance Do in Masked Discrete Diffusion Models](https://mlsanity.com/paper/2506.10971/) (2025)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [Towards Trustworthy Knowledge Graph Reasoning: An Uncertainty Aware Perspective](https://mlsanity.com/paper/2410.08985/) (2024)
- [DiffSpectra: Molecular Structure Elucidation from Spectra using Diffusion Models](https://mlsanity.com/paper/2507.06853/) (2025)
- [PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesis](https://mlsanity.com/paper/2509.12212/) (2025)
- [Synthetic Data from Diffusion Models Improve Drug Discovery Prediction](https://mlsanity.com/paper/2405.03799/) (2024)
- [Regressor-free Molecule Generation to Support Drug Response Prediction](https://mlsanity.com/paper/2405.14536/) (2024)
- [Instruction-Based Molecular Graph Generation with Unified Text-Graph Diffusion Model](https://mlsanity.com/paper/2408.09896/) (2024)
- [Backdoor Attacks on Discrete Graph Diffusion Models](https://mlsanity.com/paper/2503.06340/) (2025)
- [CDGraph: Dual Conditional Social Graph Synthesizing via Diffusion Model](https://mlsanity.com/paper/2311.01729/) (2023)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [IFH: a Diffusion Framework for Flexible Design of Graph Generative Models](https://mlsanity.com/paper/2408.13194/) (2024)
- [Robust Learning of Diffusion Models with Extremely Noisy Conditions](https://mlsanity.com/paper/2510.10149/) (2025)
- [Inference Attacks Against Graph Generative Diffusion Models](https://mlsanity.com/paper/2601.03701/) (2026)
- [Reducing Spatial Fitting Error in Distillation of Denoising Diffusion Models](https://mlsanity.com/paper/2311.03830/) (2023)

## Abstract (arXiv)

Learning the underlying distribution of molecular graphs and generating high-fidelity samples is a fundamental research problem in drug discovery and material science. However, accurately modeling distribution and rapidly generating novel molecular graphs remain crucial and challenging goals. To accomplish these goals, we propose a novel Conditional Diffusion model based on discrete Graph Structures (CDGS) for molecular graph generation. Specifically, we construct a forward graph diffusion process on both graph structures and inherent features through stochastic differential equations (SDE) and derive discrete graph structures as the condition for reverse generative processes. We present a specialized hybrid graph noise prediction model that extracts the global context and the local node-edge dependency from intermediate graph states. We further utilize ordinary differential equation (ODE) solvers for efficient graph sampling, based on the semi-linear structure of the probability flow ODE. Experiments on diverse datasets validate the effectiveness of our framework. Particularly, the proposed method still generates high-quality molecular graphs in a limited number of steps. Our code is provided in https://github.com/GRAPH-0/CDGS.