IFH: a Diffusion Framework for Flexible Design of Graph Generative Models

TL;DR

This paper proposes a graph generative model, called Insert-Fill-Halt (IFH), that supports the specification of a sequentiality degree, and evaluates the performance of IFH in terms of quality, run time, and memory, depending on different sequentiality degrees.

Abstract

Graph generative models can be classified into two prominent families: one-shot models, which generate a graph in one go, and sequential models, which generate a graph by successive additions of nodes and edges. Ideally, between these two extreme models lies a continuous range of models that adopt different levels of sequentiality. This paper proposes a graph generative model, called Insert-Fill-Halt (IFH), that supports the specification of a sequentiality degree. IFH is based upon the theory of Denoising Diffusion Probabilistic Models (DDPM), designing a node removal process that gradually destroys a graph. An insertion process learns to reverse this removal process by inserting arcs and nodes according to the specified sequentiality degree. We evaluate the performance of IFH in terms of quality, run time, and memory, depending on different sequentiality degrees. We also show that using DiGress, a diffusion-based one-shot model, as a generative step in IFH leads to improvement to the model itself, and is competitive with the current state-of-the-art.

Figures (3)

• Figure 1: Graph generation can be seen as a sequence of Node Insertions (I), Labels and Connections Filling (F), and Halting Choices (H). One-shot models fill graphs in 1 big step after choosing the number of nodes. 1-node sequential models add one node, fill its value, connect it with the remainder graph, and choose whether to stop or continue iterating. Our IFH framework can model these situations and the intermediate block sequential generation.
• Figure 2: Our Insert-Fill-Halt model. During training, a graph is corrupted (left to right) by iteratively removing nodes until the empty graph $\varnothing$ is left. At each step, the insertion (violet), filler (blue), and halt (cyan) models have to predict how many nodes were removed, what content they had, and whether the graph is terminal, respectively (right to left).
• Figure 3a: Split operation. In blue and red are the induced subgraphs ${\mathcal{G}}_A$ and ${\mathcal{G}}_B$. In green are the intermediate edges $\mathcal{E}_{AB},\mathcal{E}_{BA}$. On the right is the split adjacency matrix, with the same coloring.

Theorems & Definitions (11)

• Definition 1: Remove operation
• Definition 2: Induced subgraph
• Definition 3: Split operation
• Definition 4: Merge operation
• Definition 5: Forward and reversed removal sequence
• Definition 6: Halting process
• proof
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