# Diffusion-Free Graph Generation with Next-Scale Prediction

arXiv: https://arxiv.org/abs/2503.23612 · HTML: https://mlsanity.com/paper/2503.23612/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 30 references that are in the map.
- First posted on arXiv 30 Mar 2025.

## Builds on (most cited first, 24 of 24)

- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [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)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [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)
- [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)
- [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)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Beyond Next-Token: Next-X Prediction for Autoregressive Visual Generation](https://mlsanity.com/paper/2502.20388/) (2025)
- [Efficient and Scalable Graph Generation through Iterative Local Expansion](https://mlsanity.com/paper/2312.11529/) (2023)
- [Order Matters: Probabilistic Modeling of Node Sequence for Graph Generation](https://mlsanity.com/paper/2106.06189/) (2021)
- [SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generation](https://mlsanity.com/paper/2307.01646/) (2023)
- [Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation](https://mlsanity.com/paper/2402.03687/) (2024)
- [FlexVAR: Flexible Visual Autoregressive Modeling without Residual Prediction](https://mlsanity.com/paper/2502.20313/) (2025)

## Built on by (most cited first, 3 of 3)

- [Multi-scale Autoregressive Models are Laplacian, Discrete, and Latent Diffusion Models in Disguise](https://mlsanity.com/paper/2510.02826/) (2025)
- [UMEDA: Unified Multi-modal Efficient Data Fusion for Privacy-Preserving Graph Federated Learning via Spectral-Gated Attention and Diffusion-Based Operator Alignment](https://mlsanity.com/paper/2605.08288/) (2026)
- [Scaling Novel Graph Generation via Lightweight Structure-Guided Autoregressive Models](https://mlsanity.com/paper/2606.04287/) (2026)

## Abstract (arXiv)

Autoregressive models excel in efficiency and plug directly into the transformer ecosystem, delivering robust generalization, predictable scalability, and seamless workflows such as fine-tuning and parallelized training. However, they require an explicit sequence order, which contradicts the unordered nature of graphs. In contrast, diffusion models maintain permutation invariance and enable one-shot generation but require up to thousands of denoising steps and additional features for expressivity, leading to high computational costs. Inspired by recent breakthroughs in image generation, especially the success of visual autoregressive methods, we propose MAG, a novel diffusion-free graph generation framework based on next-scale prediction. By leveraging a hierarchy of latent representations, the model progressively generates scales of the entire graph without the need for explicit node ordering. Experiments on both generic and molecular graph datasets demonstrated the potential of this method, achieving inference speedups of up to three orders of magnitude over state-of-the-art methods, while preserving high-quality generation.