Unpaired Joint Distribution Modeling via Multi-Scale Image Representations
For practitioners in cryo-EM and other domains requiring joint distribution modeling from unpaired data, this method provides a principled approach with theoretical guarantees.
This work tackles the ill-posed problem of learning a joint distribution from marginal observations. The proposed LUD-MSR framework models the joint distribution via multi-scale representations and achieves effective denoising on cryo-EM benchmarks, outperforming existing methods.
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.