# LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening

arXiv: https://arxiv.org/abs/2512.01190 · HTML: https://mlsanity.com/paper/2512.01190/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 25 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 23 of 23)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [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)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [DeFoG: Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2410.04263/) (2024)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generation](https://mlsanity.com/paper/2001.08184/) (2020)
- [Scalable Deep Generative Modeling for Sparse Graphs](https://mlsanity.com/paper/2006.15502/) (2020)
- [Spectrally approximating large graphs with smaller graphs](https://mlsanity.com/paper/1802.07510/) (2018)
- [Graph Generation with Diffusion Mixture](https://mlsanity.com/paper/2302.03596/) (2023)
- [Efficient and Scalable Graph Generation through Iterative Local Expansion](https://mlsanity.com/paper/2312.11529/) (2023)
- [Cometh: A continuous-time discrete-state graph diffusion model](https://mlsanity.com/paper/2406.06449/) (2024)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Improving Molecular Graph Generation with Flow Matching and Optimal Transport](https://mlsanity.com/paper/2411.05676/) (2024)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [An Unpooling Layer for Graph Generation](https://mlsanity.com/paper/2206.01874/) (2022)

## Built on by (most cited first, 2 of 2)

- [When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors](https://mlsanity.com/paper/2610.13765/) (2026)
- [Your Discrete Graph Diffusion Model is Secretly Memorizing](https://mlsanity.com/paper/2610.13786/) (2026)

## Abstract (arXiv)

Graph generation is a critical task across scientific domains. Existing methods fall broadly into two categories: autoregressive models, which iteratively expand graphs, and one-shot models, such as diffusion, which generate the full graph at once. In this work, we provide an analysis of these two paradigms and reveal a key trade-off: autoregressive models stand out in capturing fine-grained local structures, such as degree and clustering properties, whereas one-shot models excel at modeling global patterns, such as spectral distributions. Building on this, we propose LGDC (latent graph diffusion via spectrum-preserving coarsening), a hybrid framework that combines strengths of both approaches. LGDC employs a spectrum-preserving coarsening-decoarsening to bidirectionally map between graphs and a latent space, where diffusion efficiently generates latent graphs before expansion restores detail. This design captures both local and global properties with improved efficiency. Empirically, LGDC matches autoregressive models on locally structured datasets (Tree) and diffusion models on globally structured ones (Planar, Community-20), validating the benefits of hybrid generation.