Multiobjective Distribution Matching

Distribution matching is a core concept in machine learning, with applications in generative models, domain adaptation, and algorithmic fairness. A closely related but less explored challenge is generating a distribution that aligns with multiple underlying distributions, often with conflicting objectives, known as a Pareto optimal distribution. In this paper, we develop a general theory based on information geometry to construct the Pareto set and front for the entire exponential family under KL and inverse KL divergences. This formulation allows explicit derivation of the Pareto set and front for multivariate normal distributions, enabling applications like multiobjective variational autoencoders (MOVAEs) to generate interpolated image distributions. Experimental results on real-world images demonstrate that both algorithms can generate high-quality interpolated images across multiple distributions. © 2025 by the author(s).