# Graph Generation with Diffusion Mixture

arXiv: https://arxiv.org/abs/2302.03596 · HTML: https://mlsanity.com/paper/2302.03596/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 58 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [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)
- [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)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (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)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)

## Built on by (most cited first, 30 of 55)

- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Cometh: A continuous-time discrete-state graph diffusion model](https://mlsanity.com/paper/2406.06449/) (2024)
- [Continuous Diffusion Model for Language Modeling](https://mlsanity.com/paper/2502.11564/) (2025)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)
- [Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes](https://mlsanity.com/paper/2310.07216/) (2023)
- [Graph Generative Pre-trained Transformer](https://mlsanity.com/paper/2501.01073/) (2025)
- [Graph Diffusion Policy Optimization](https://mlsanity.com/paper/2402.16302/) (2024)
- [Advancing Graph Generation through Beta Diffusion](https://mlsanity.com/paper/2406.09357/) (2024)
- [Geometric Representation Condition Improves Equivariant Molecule Generation](https://mlsanity.com/paper/2410.03655/) (2024)
- [Flatten Graphs as Sequences: Transformers are Scalable Graph Generators](https://mlsanity.com/paper/2502.02216/) (2025)
- [Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation](https://mlsanity.com/paper/2503.21592/) (2025)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matching](https://mlsanity.com/paper/2502.15805/) (2025)
- [Learning Flexible Forward Trajectories for Masked Molecular Diffusion](https://mlsanity.com/paper/2505.16790/) (2025)
- [Conditional Synthesis of 3D Molecules with Time Correction Sampler](https://mlsanity.com/paper/2411.00551/) (2024)
- [Joint Generative Modeling of Grounded Scene Graphs and Images via Diffusion Models](https://mlsanity.com/paper/2401.01130/) (2024)
- [Any-Property-Conditional Molecule Generation with Self-Criticism using Spanning Trees](https://mlsanity.com/paper/2407.09357/) (2024)
- [Do Graph Diffusion Models Accurately Capture and Generate Substructure Distributions?](https://mlsanity.com/paper/2502.02488/) (2025)
- [Explain with Visual Keypoints Like a Real Mentor! A Benchmark for Multimodal Solution Explanation](https://mlsanity.com/paper/2504.03197/) (2025)
- [Generating Directed Graphs with Dual Attention and Asymmetric Encoding](https://mlsanity.com/paper/2506.16404/) (2025)
- [Flowette: Flow Matching with Graphette Priors for Graph Generation](https://mlsanity.com/paper/2602.23566/) (2026)
- [HybridLinker: Topology-Guided Posterior Sampling for Enhanced Diversity and Validity in 3D Molecular Linker Generation](https://mlsanity.com/paper/2502.17349/) (2025)
- [SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion](https://mlsanity.com/paper/2508.14352/) (2025)
- [Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction](https://mlsanity.com/paper/2510.04522/) (2025)
- [Rethinking Metrics and Diffusion Architecture for 3D Point Cloud Generation](https://mlsanity.com/paper/2511.05308/) (2025)
- [LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening](https://mlsanity.com/paper/2512.01190/) (2025)
- [Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation](https://mlsanity.com/paper/2603.28572/) (2026)
- [Hierarchical Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2604.00236/) (2026)
- [G2T-LLM: Graph-to-Tree Text Encoding for Molecule Generation with Fine-Tuned Large Language Models](https://mlsanity.com/paper/2410.02198/) (2024)

## Abstract (arXiv)

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.