Copula Diffusion Modelling Under Marginal Constraints

Laura Battaglia, Tyler Farghly, Stefano Cortinovis, Daniel de Vassimon Manela, Amitis Shidani, Christopher Williams

Keywords: Copulas, Diffusion Models, Probabilistic Modelling, Marginal Inference

TL;DR: We explore the use of generative diffusion models to learn copula densities using marginal regularisation methods and improved diffusion scheduling.

Abstract: Modelling complex multivariate distributions often requires trade-offs between expressivity, tractability, and control over marginal behavior. Copula models offer a principled way to decouple marginals from dependencies, but existing approaches either rely on restrictive parametric families or forgo strict marginal constraints. In this work, we show that diffusion models can be adapted to learn copula representations that preserve uniform marginals through explicit regularisation. To this end, we augment the training objective with (i) a Monte Carlo penalty that encourages the learned score to match the theoretical score of a uniform distribution throughout the diffusion process and (ii) recent advances in online diffusion schedule optimisation. Experiments on synthetic bivariate data show that our method improves sample quality and reliably enforces marginal uniformity, supporting its effectiveness for copula estimation.

Submission Number: 7