Motivation • Graphs used as an abstract language throughout modern STEM • Can encode discrete structures — molecules, social networks, etc. Problem setup A graph \( G \) over \( n \) vertices is represented as: \( G = (X,A), X \in \mathbb{R}^{n \times d}, A \in \{0, 1\}^{n \times n} \) Goal: learn a distribution over graphs and generate novel, faithful samples. Classical generative models and their limitations: • VAEs (Simonovsky and Komodakis, 2018) — expensive graph-matching for permutation invariance • GANs (Wang et al., 2018) — mode collapse (reduction of diversity) • Normalising flows (Luo, Yan, and Ji, 2021) — constrained to bijective mappings Diffusion models have emerged as a compelling alternative.

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Coursework for the Applications of Neural Networks Theory MFF UK module.