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This paper addresses the challenge of learning a joint distribution from marginal observations, which is complicated by the ambiguity of feasible couplings. The authors introduce LUD-MSR, a latent-variable probabilistic framework that leverages Multi-Scale image Representations to optimize evidence lower bounds using only marginal data, revealing a trade-off between domain consistency and information preservation. Experimental results on cryo-electron microscopy denoising benchmarks show that LUD-MSR outperforms existing methods in achieving a better balance of this trade-off.
Achieving a superior balance between domain consistency and information preservation in joint distribution modeling could redefine approaches to unpaired data scenarios.
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.
