Geometric & Graph Generative AI

Overview

We investigate the fundamental limits of learning and information processing for geometric data. Our goal is to develop theoretically grounded generative models that can handle the complexity of 3D structures and molecular graphs.

Active Projects

1. Autoregressive Expansion for Latent Graph Diffusion

Goal: Extend Latent Graph Diffusion (LGDC) by introducing an autoregressive expansion mechanism. Details: Instead of expanding all nodes in a single step, this project generates fine-level structure iteratively, allowing local decisions to be conditioned on previously generated substructures.

2. Grounding Geometric Generative Models

Goal: Leverage discrete differential geometry to build better generative models. Details: We view graphs as samples from an underlying manifold. This project derives new families of diffusion and flow-based models grounded in curvature approximations and stochastic differential equations on manifolds.

LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening
N Osman, K Jiang, D Buffelli, X Dong, L Toni. NeurIPS 2025 Workshop.
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Effects of Random Edge-Dropping on Over-Squashing in Graph Neural Networks
J Singh, K Jiang, B Paige, L Toni. NeurIPS 2025.
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Bures-Wasserstein Flow Matching for Graph Generation
K Jiang, J Cui, X Dong, L Toni. Submitted to ICLR, 2025.
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From In Silico to In Vitro: Evaluating Molecule Generative Models
N Osman, V Lembo, G Bottegoni, L Toni. NeurIPS 2025 AI4Science Workshop.
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Midi: Mixed graph and 3d denoising diffusion for molecule generation
C Vignac, N Osman, L Toni, P Frossard. ECML PKDD 2023.
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Heterogeneous Graph Structure Learning through the Lens of Data-generating Processes
K Jiang, B Tang, X Dong, L Toni. AISTATS 2025.
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Generative AI Graph Learning