Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets that demonstrates GLAD as the first equivariant latent graph generative method achieves competitive performance with the state of the art baselines.

Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies of the noisy distributions across time of these models lead to error accumulation and propagation during the reverse denoising process—a phenomenon known as \emph{compounding denoising errors}. To address this problem, we propose a novel framework called \emph{Simple Iterative Denoising}, which simplifies discrete diffusion and circumvents the issue by removing dependencies on previous intermediate states in the noising process. Additionally, we enhance our model by incorporating a \emph{Critic}, which during generation selectively retains or corrupts elements in an instance based on their likelihood under the data distribution. Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.