仅用边缘数据学习联合分布，通过多尺度表征提升建模精度。
Unpaired Joint Distribution Modeling via Multi-Scale Image Representations
- 基于潜在变量框架，利用辅助表征优化证据下界。
- 在冷冻电镜等真实去噪任务中显著提升分布逼近效果。
- 多尺度表征平衡领域一致性与信息保留，适合图像生成任务。
本文研究从边际观测中学习联合分布的问题，该问题因可行耦合的不确定性而本质病态。我们提出LUD-MSR，一种基于潜在变量的概率框架，通过辅助表示建模联合分布，并仅使用边际数据优化证据下界。在温和假设下，建立了分布近似误差的上界。分析揭示了表示学习中领域一致性与信息保留之间的权衡。为解决此权衡，引入多尺度图像表示（MSR）映射，利用粗尺度结构相似性，同时抑制领域特异性变化。实验表明，相较于现有方法，MSR实现了更优的权衡。在真实世界去噪基准（包括冷冻电镜，cryo-EM）上验证了该框架的有效性。
原文摘要 · Abstract (English)
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.
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