Principled Latent Diffusion for Graphs via Laplacian Autoencoders
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| Format: | Preprint |
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2026
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| _version_ | 1866911672601411584 |
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| author | Siraudin, Antoine Morris, Christopher |
| author_facet | Siraudin, Antoine Morris, Christopher |
| contents | Graph diffusion models achieve state-of-the-art performance in graph generation but suffer from quadratic complexity in the number of nodes -- and much of their capacity is wasted modeling the absence of edges in sparse graphs. Inspired by latent diffusion in other modalities, a natural idea is to compress graphs into a low-dimensional latent space and perform diffusion in that space. However, unlike images or text, graph generation requires nearly lossless reconstruction, as even a single error in decoding an adjacency matrix can render the entire sample invalid. This challenge has remained largely unaddressed. We propose LG-Flow, a latent graph diffusion framework that directly overcomes these obstacles. A permutation-equivariant autoencoder maps nodes to fixed-dimensional embeddings that enable near-lossless reconstruction of both undirected graphs and DAGs. The dimensionality of this latent representation scales linearly with the number of nodes, thereby removing the quadratic adjacency-space bottleneck in the diffusion process and enabling the training of substantially larger generative backbones. In this latent space, we train a Diffusion Transformer with flow matching, enabling efficient and expressive graph generation. Our approach achieves competitive results against state-of-the-art graph diffusion models while delivering up to a $1000\times$ speed-up. Our code is available at https://github.com/asiraudin/LG-Flow . |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13780 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Principled Latent Diffusion for Graphs via Laplacian Autoencoders Siraudin, Antoine Morris, Christopher Machine Learning Graph diffusion models achieve state-of-the-art performance in graph generation but suffer from quadratic complexity in the number of nodes -- and much of their capacity is wasted modeling the absence of edges in sparse graphs. Inspired by latent diffusion in other modalities, a natural idea is to compress graphs into a low-dimensional latent space and perform diffusion in that space. However, unlike images or text, graph generation requires nearly lossless reconstruction, as even a single error in decoding an adjacency matrix can render the entire sample invalid. This challenge has remained largely unaddressed. We propose LG-Flow, a latent graph diffusion framework that directly overcomes these obstacles. A permutation-equivariant autoencoder maps nodes to fixed-dimensional embeddings that enable near-lossless reconstruction of both undirected graphs and DAGs. The dimensionality of this latent representation scales linearly with the number of nodes, thereby removing the quadratic adjacency-space bottleneck in the diffusion process and enabling the training of substantially larger generative backbones. In this latent space, we train a Diffusion Transformer with flow matching, enabling efficient and expressive graph generation. Our approach achieves competitive results against state-of-the-art graph diffusion models while delivering up to a $1000\times$ speed-up. Our code is available at https://github.com/asiraudin/LG-Flow . |
| title | Principled Latent Diffusion for Graphs via Laplacian Autoencoders |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.13780 |