# Unifying Generation and Prediction on Graphs with Latent Graph Diffusion

arXiv: https://arxiv.org/abs/2402.02518 · HTML: https://mlsanity.com/paper/2402.02518/

## Key facts

- Cited by 25 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 75 of its 83 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## 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, 30 of 75)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)

## Built on by (most cited first, 25 of 25)

- [ArtFormer: Controllable Generation of Diverse 3D Articulated Objects](https://mlsanity.com/paper/2412.07237/) (2024)
- [Geometric Representation Condition Improves Equivariant Molecule Generation](https://mlsanity.com/paper/2410.03655/) (2024)
- [Generating Graphs via Spectral Diffusion](https://mlsanity.com/paper/2402.18974/) (2024)
- [Decoupling High and Low Frequencies for Faithful Image Generation with Fine Details](https://mlsanity.com/paper/2509.05441/) (2025)
- [Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation](https://mlsanity.com/paper/2602.15022/) (2026)
- [Toward Graph-Tokenizing Large Language Models with Reconstructive Graph Instruction Tuning](https://mlsanity.com/paper/2603.01385/) (2026)
- [Graph Guided Diffusion: Unified Guidance for Conditional Graph Generation](https://mlsanity.com/paper/2505.19685/) (2025)
- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [Flowette: Flow Matching with Graphette Priors for Graph Generation](https://mlsanity.com/paper/2602.23566/) (2026)
- [Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction](https://mlsanity.com/paper/2510.04522/) (2025)
- [Transport-Coupled Bayesian Flows for Molecular Graph Generation](https://mlsanity.com/paper/2510.10211/) (2025)
- [Variational Bayesian Flow Network for Graph Generation](https://mlsanity.com/paper/2601.22524/) (2026)
- [FlashMol: High-Quality Molecule Generation in as Few as Four Steps](https://mlsanity.com/paper/2605.07020/) (2026)
- [Codebook Agent: Amortized Topology Design for LLM Multi-Agent Systems](https://mlsanity.com/paper/2609.02264/) (2026)
- [ReDiSC: A Reparameterized Masked Diffusion Model for Scalable Node Classification with Structured Predictions](https://mlsanity.com/paper/2507.14484/) (2025)
- [BadGraph: A Backdoor Attack Against Latent Diffusion Model for Text-Guided Graph Generation](https://mlsanity.com/paper/2510.20792/) (2025)
- [Geometry-Guided Generative Representation for Functional Brain Graphs](https://mlsanity.com/paper/2511.04539/) (2025)
- [Routing by Reaching: Composition of Pre-trained GFlowNets for Multi-Objective Generation](https://mlsanity.com/paper/2602.21565/) (2026)
- [GCCM: Enhancing Generative Graph Prediction via Contrastive Consistency Model](https://mlsanity.com/paper/2605.05689/) (2026)
- [Generating Graph-Like Logical Rules for Knowledge Graph Reasoning via Diffusion Models](https://mlsanity.com/paper/2605.30747/) (2026)
- [Efficient Synthetic Network Generation via Latent Embedding Reconstruction](https://mlsanity.com/paper/2606.00934/) (2026)
- [3D Scene Graph Prediction: Generating Hierarchical Models from Partially Observed Environments](https://mlsanity.com/paper/2607.10879/) (2026)
- [Partially Observed Sparse Graphs: The Unknown Sampling Rate is a Tail Index](https://mlsanity.com/paper/2609.26199/) (2026)
- [GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations](https://mlsanity.com/paper/2609.35527/) (2026)
- [Efficient Graph Generation via Direct Prediction and Flow Matching](https://mlsanity.com/paper/2610.05397/) (2026)

## Abstract (arXiv)

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) using one formulation. We first formulate prediction tasks including regression and classification into a generic (conditional) generation framework, which enables diffusion models to perform deterministic tasks with provable guarantees. We then propose Latent Graph Diffusion (LGD), a generative model that can generate node, edge, and graph-level features of all categories simultaneously. We achieve this goal by embedding the graph structures and features into a latent space leveraging a powerful encoder and decoder, then training a diffusion model in the latent space. LGD is also capable of conditional generation through a specifically designed cross-attention mechanism. Leveraging LGD and the ``all tasks as generation'' formulation, our framework is capable of solving graph tasks of various levels and types. We verify the effectiveness of our framework with extensive experiments, where our models achieve state-of-the-art or highly competitive results across a wide range of generation and regression tasks.