Unpaired Joint Distribution Modeling via Multi-Scale Image Representations

2026-07-09

AI Summary

Learning joint distributions from marginal observations is inherently ill-posed due to the ambiguity in feasible couplings. This work proposes the LUD-MSR framework, which models the joint distribution by introducing auxiliary latent variables and optimizes a variational evidence lower bound using only marginal data. A key innovation is the incorporation of multi-scale image representations (MSR) to jointly balance the trade-off between domain consistency and information preservation. By integrating structural similarity modeling, the method achieves substantial improvements over existing approaches on real-world image denoising tasks, including cryo-electron microscopy images, thereby demonstrating its effectiveness and practical utility.

Abstract

This paper studies the problem of learning a joint distribution from marginal observations, which is inherently ill-posed due to the ambiguity of feasible couplings. We propose LUD-MSR, a latent-variable probabilistic framework that models the joint distribution via auxiliary representations and optimizes evidence lower bounds using only marginal data. Under mild assumptions, we establish an upper bound on the distribution approximation error. This analysis reveals a trade-off in representation learning between domain consistency and information preservation. To address this trade-off, we introduce a Multi-Scale image Representation (MSR) mapping that exploits structural similarity at coarse scales while suppressing domain-specific variations. We show that MSR achieves a more favorable balance of this trade-off compared to existing approaches. Experiments on real-world denoising benchmarks, including cryo-electron microscopy (cryo-EM), demonstrate the effectiveness of the proposed framework.

Problem

• joint distribution
• marginal observations
• unpaired learning
• distribution modeling
• ill-posed problem

Innovation

• multi-scale representation
• joint distribution modeling
• unpaired learning
• latent-variable model
• domain consistency