# CDGraph: Dual Conditional Social Graph Synthesizing via Diffusion Model

arXiv: https://arxiv.org/abs/2311.01729 · HTML: https://mlsanity.com/paper/2311.01729/

## Key facts

- Cited by 2 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 16 of its 25 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## 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, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (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)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [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)
- [Step-unrolled Denoising Autoencoders for Text Generation](https://mlsanity.com/paper/2112.06749/) (2021)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [NeVAE: A Deep Generative Model for Molecular Graphs](https://mlsanity.com/paper/1802.05283/) (2018)
- [Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation](https://mlsanity.com/paper/2301.00427/) (2023)
- [Generating Simple Directed Social Network Graphs for Information Spreading](https://mlsanity.com/paper/2205.02485/) (2022)
- [When Social Influence Meets Item Inference](https://mlsanity.com/paper/1502.07439/) (2015)

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

- [Generating Directed Graphs with Dual Attention and Asymmetric Encoding](https://mlsanity.com/paper/2506.16404/) (2025)
- [DMol: A Highly Efficient and Chemical Motif-Preserving Molecule Generation Platform](https://mlsanity.com/paper/2504.06312/) (2025)

## Abstract (arXiv)

The social graphs synthesized by the generative models are increasingly in demand due to data scarcity and concerns over user privacy. One of the key performance criteria for generating social networks is the fidelity to specified conditionals, such as users with certain membership and financial status. While recent diffusion models have shown remarkable performance in generating images, their effectiveness in synthesizing graphs has not yet been explored in the context of conditional social graphs. In this paper, we propose the first kind of conditional diffusion model for social networks, CDGraph, which trains and synthesizes graphs based on two specified conditions. We propose the co-evolution dependency in the denoising process of CDGraph to capture the mutual dependencies between the dual conditions and further incorporate social homophily and social contagion to preserve the connectivity between nodes while satisfying the specified conditions. Moreover, we introduce a novel classifier loss, which guides the training of the diffusion process through the mutual dependency of dual conditions. We evaluate CDGraph against four existing graph generative methods, i.e., SPECTRE, GSM, EDGE, and DiGress, on four datasets. Our results show that the generated graphs from CDGraph achieve much higher dual-conditional validity and lower discrepancy in various social network metrics than the baselines, thus demonstrating its proficiency in generating dual-conditional social graphs.