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[2601.13780] Principled Latent Diffusion for Graphs via Laplacian Autoencoders
Summary
This paper presents LG-Flow, a novel latent graph diffusion framework that enhances graph generation efficiency by compressing graphs into a low-dimensional latent space, enabling near-lossless reconstruction and significant speed improvements.
Why It Matters
Graph diffusion models are crucial for various applications in machine learning, but they often face scalability issues due to quadratic complexity. The LG-Flow framework addresses these challenges, making it feasible to train larger models while maintaining performance, which is essential for advancing research in graph-based machine learning.
Key Takeaways
- LG-Flow compresses graphs into a low-dimensional latent space for efficient diffusion.
- The framework allows for near-lossless reconstruction of graphs, addressing a key challenge in graph generation.
- Achieves competitive results against state-of-the-art models while providing up to 1000x speed improvements.
Computer Science > Machine Learning arXiv:2601.13780 (cs) [Submitted on 20 Jan 2026 (v1), last revised 25 Feb 2026 (this version, v2)] Title:Principled Latent Diffusion for Graphs via Laplacian Autoencoders Authors:Antoine Siraudin, Christopher Morris View a PDF of the paper titled Principled Latent Diffusion for Graphs via Laplacian Autoencoders, by Antoine Siraudin and 1 other authors View PDF HTML (experimental) Abstract: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 there. 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 each node into a fixed-dimensional embedding from which the full adjacency is provably recoverable, enabling near-lossless reconstruction for both undirected graphs and DAGs. The dimensionality of this latent representation scales linearly with the number of nodes, eliminating the quadratic bottleneck and making it f...
