Generative Modeling of Discrete Joint Distributions by E-Geodesic Flow Matching on Assignment Manifolds

Understand

This paper introduces a novel generative model for discrete distributions based on continuous normalizing flows on the submanifold of factorizing discrete measures.

• Integration of the flow gradually assigns categories and avoids issues of discretizing the latent continuous model like rounding, sample truncation etc.
• General non-factorizing discrete distributions capable of representing complex statistical dependencies of structured discrete data, can be approximated by embedding the submanifold into a the meta-simplex of all joint discrete distributions and data-driven averaging.
• Efficient training of the generative model is demonstrated by matching the flow of geodesics of factorizing discrete distributions.