Built on

B. D. Anderson, “Reverse-time diffusion equation models,” Stochastic Processes and their Applications , vol. 12, no. 3, pp. 313–326, 1982
1982
Earlier work this paper cites.
F. Costa and K. De Grave, “Fast neighborhood subgraph pairwise distance kernel,” in ICML , 2010
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P. Vincent, “A connection between score matching and denoising autoencoders,” Neural Comput. , vol. 23, no. 7, p. 1661–1674, Jrul 2011
2011
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J. J. Irwin, T. Sterling, M. M. Mysinger, E. S. Bolstad, and R. G. Coleman, “Zinc: a free tool to discover chemistry for biology,” Journal of chemical information and modeling , vol. 52, no. 7, pp. 1757–1768, 2012
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R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. Von Lilienfeld, “Quantum chemistry structures and properties of 134 kilo molecules,” Scientific data , vol. 1, no. 1, pp. 1–7, 2014
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J. You, R. Ying, X. Ren, W. Hamilton, and J. Leskovec, “Graphrnn: Generating realistic graphs with deep auto-regressive models,” in ICMLg , 2018, pp. 5708–5717
2018
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N. De Cao and T. Kipf, “Molgan: An implicit generative model for small molecular graphs,” arXiv preprint arXiv:1805.11973 , 2018
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2018
Earlier work this paper cites.
T. Ma, J. Chen, and C. Xiao, “Constrained generation of semantically valid graphs via regularizing variational autoencoders,” in NeurIPS , 2018
2018
Earlier work this paper cites.

Similar

Y. Li, O. Vinyals, C. Dyer, R. Pascanu, and P. Battaglia, “Learning deep generative models of graphs,” arXiv preprint arXiv:1803.03324 , 2018
Original
2018
Cited alongside, same era.
K. Preuer, P. Renz, T. Unterthiner, S. Hochreiter, and G. Klambauer, “Fréchet chemnet distance: a metric for generative models for molecules in drug discovery,” Journal of chemical information and modeling , vol. 58, no. 9, pp. 1736–1741, 2018
2018
Cited alongside, same era.
H. Wang, T. Xu, Q. Liu, D. Lian, E. Chen, D. Du, H. Wu, and W. Su, “Mcne: an end-to-end framework for learning multiple conditional network representations of social network,” in KDD , 2019, pp. 1064–1072
2019
Cited alongside, same era.
H. Wang, J. Wang, J. Wang, M. Zhao, W. Zhang, F. Zhang, W. Li, X. Xie, and M. Guo, “Learning graph representation with generative adversarial nets,” IEEE Transactions on Knowledge and Data Engineering , vol. 33, no. 8, pp. 3090–3103, 2019
2019
Cited alongside, same era.

Then

Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, “Score-based generative modeling through stochastic differential equations,” arXiv preprint arXiv:2011.13456 , 2020
Original
2020
Later among the works it cites.
X. Guo and L. Zhao, “A systematic survey on deep generative models for graph generation,” arXiv preprint arXiv:2007.06686 , 2020
Original
2020
Later among the works it cites.
C. Liu, L. Zhu, and M. Belkin, “Toward a theory of optimization for over-parameterized systems of non-linear equations: the lessons of deep learning,” CoRR , vol. abs/2003.00307, 2020
Original
2020
Later among the works it cites.
H. Lee, E. Hyung, and S. J. Hwang, “Rapid neural architecture search by learning to generate graphs from datasets,” arXiv preprint arXiv:2107.00860 , 2021
Original
2021
Later among the works it cites.

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2022

Fast Graph Generation via Spectral Diffusion

Luo, Tianze, Mo, Zhanfeng, Pan, Sinno Jialin

Understand

Generating graph-structured data is a challenging problem, which requires learning the underlying distribution of graphs.

Various models such as graph VAE, graph GANs, and graph diffusion models have been proposed to generate meaningful and reliable graphs, among which the diffusion models have achieved state-of-the-art performance.
In this paper, we argue that running full-rank diffusion SDEs on the whole graph adjacency matrix space hinders diffusion models from learning graph topology generation, and hence significantly deteriorates the quality of generated graph data.
To address this limitation, we propose an efficient yet effective Graph Spectral Diffusion Model (GSDM), which is driven by low-rank diffusion SDEs on the graph spectrum space.

Built on

B. D. Anderson, “Reverse-time diffusion equation models,” Stochastic Processes and their Applications , vol. 12, no. 3, pp. 313–326, 1982
1982
Earlier work this paper cites.
F. Costa and K. De Grave, “Fast neighborhood subgraph pairwise distance kernel,” in ICML , 2010
2010
Earlier work this paper cites.
P. Vincent, “A connection between score matching and denoising autoencoders,” Neural Comput. , vol. 23, no. 7, p. 1661–1674, Jrul 2011
2011
Earlier work this paper cites.
J. J. Irwin, T. Sterling, M. M. Mysinger, E. S. Bolstad, and R. G. Coleman, “Zinc: a free tool to discover chemistry for biology,” Journal of chemical information and modeling , vol. 52, no. 7, pp. 1757–1768, 2012
2012
Earlier work this paper cites.
R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. Von Lilienfeld, “Quantum chemistry structures and properties of 134 kilo molecules,” Scientific data , vol. 1, no. 1, pp. 1–7, 2014
2014
Earlier work this paper cites.
G. Landrum et al. , “Rdkit: Open-source cheminformatics software,” 2016. [Online]. Available: http://www.rdkit.org/
2016
Earlier work this paper cites.
M. Simonovsky and N. Komodakis, “Graphvae: Towards generation of small graphs using variational autoencoders,” in ICANN , 2018, pp. 412–422
2018
Earlier work this paper cites.
J. You, R. Ying, X. Ren, W. Hamilton, and J. Leskovec, “Graphrnn: Generating realistic graphs with deep auto-regressive models,” in ICMLg , 2018, pp. 5708–5717
2018
Earlier work this paper cites.
N. De Cao and T. Kipf, “Molgan: An implicit generative model for small molecular graphs,” arXiv preprint arXiv:1805.11973 , 2018
Original
2018
Earlier work this paper cites.
T. Ma, J. Chen, and C. Xiao, “Constrained generation of semantically valid graphs via regularizing variational autoencoders,” in NeurIPS , 2018
2018
Earlier work this paper cites.

Similar

Y. Li, O. Vinyals, C. Dyer, R. Pascanu, and P. Battaglia, “Learning deep generative models of graphs,” arXiv preprint arXiv:1803.03324 , 2018
Original
2018
Cited alongside, same era.
K. Preuer, P. Renz, T. Unterthiner, S. Hochreiter, and G. Klambauer, “Fréchet chemnet distance: a metric for generative models for molecules in drug discovery,” Journal of chemical information and modeling , vol. 58, no. 9, pp. 1736–1741, 2018
2018
Cited alongside, same era.
H. Wang, T. Xu, Q. Liu, D. Lian, E. Chen, D. Du, H. Wu, and W. Su, “Mcne: an end-to-end framework for learning multiple conditional network representations of social network,” in KDD , 2019, pp. 1064–1072
2019
Cited alongside, same era.
H. Wang, J. Wang, J. Wang, M. Zhao, W. Zhang, F. Zhang, W. Li, X. Xie, and M. Guo, “Learning graph representation with generative adversarial nets,” IEEE Transactions on Knowledge and Data Engineering , vol. 33, no. 8, pp. 3090–3103, 2019
2019
Cited alongside, same era.

Then

Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, “Score-based generative modeling through stochastic differential equations,” arXiv preprint arXiv:2011.13456 , 2020
Original
2020
Later among the works it cites.
X. Guo and L. Zhao, “A systematic survey on deep generative models for graph generation,” arXiv preprint arXiv:2007.06686 , 2020
Original
2020
Later among the works it cites.
C. Liu, L. Zhu, and M. Belkin, “Toward a theory of optimization for over-parameterized systems of non-linear equations: the lessons of deep learning,” CoRR , vol. abs/2003.00307, 2020
Original
2020
Later among the works it cites.
H. Lee, E. Hyung, and S. J. Hwang, “Rapid neural architecture search by learning to generate graphs from datasets,” arXiv preprint arXiv:2107.00860 , 2021
Original
2021
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Y. Song and S. Ermon, Generative Modeling by Estimating Gradients of the Data Distribution . Red Hook, NY, USA: Curran Associates Inc., 2019

2019

Cited alongside, same era.

J. Liu, A. Kumar, J. Ba, J. Kiros, and K. Swersky, “Graph normalizing flows,” in NeurIPS , 2019

2019

Cited alongside, same era.

Y. Yang, Z. Feng, M. Song, and X. Wang, “Factorizable graph convolutional networks,” in NeurIPS , 2020, pp. 20 286–20 296

2020

Cited alongside, same era.

C. Zang and F. Wang, “Moflow: an invertible flow model for generating molecular graphs,” in KDD , 2020, pp. 617–626

2020

Cited alongside, same era.

C. Shi, M. Xu, Z. Zhu, W. Zhang, M. Zhang, and J. Tang, “Graphaf: a flow-based autoregressive model for molecular graph generation,” arXiv preprint arXiv:2001.09382 , 2020

Original

2020

Cited alongside, same era.

C. Niu, Y. Song, J. Song, S. Zhao, A. Grover, and S. Ermon, “Permutation invariant graph generation via score-based generative modeling,” in AISTATS , 2020, pp. 4474–4484

2020

Cited alongside, same era.

H. Liu, L. Jing, J. Wen, P. Xu, J. Wang, J. Yu, and M. K. Ng, “Interpretable deep generative recommendation models.” J. Mach. Learn. Res. , vol. 22, pp. 202–1, 2021

2021

Later among the works it cites.

Y. Luo, K. Yan, and S. Ji, “Graphdf: A discrete flow model for molecular graph generation,” in ICML , 2021, pp. 7192–7203

2021

Later among the works it cites.

M. Liu, K. Yan, B. Oztekin, and S. Ji, “Graphebm: Molecular graph generation with energy-based models,” arXiv preprint arXiv:2102.00546 , 2021

Original

2021

Later among the works it cites.

A. Nichol and P. Dhariwal, “Improved denoising diffusion probabilistic models,” CoRR , vol. abs/2102.09672, 2021

Original

2021