用潜在空间分布匹配提升半监督图像生成质量
Semi-Supervised Generative Learning via Latent Space Distribution Matching
- 先学低维潜在空间，再用配对数据匹配联合分布
- 仅用配对数据实现高质量生成，提升几何保真度
- 适合研究生成模型与扩散模型理论的学者
我们提出潜在空间分布匹配（LSDM），一种用于条件分布半监督生成建模的新框架。LSDM分两步进行：(i) 从配对与未配对数据中学习低维潜在空间；(ii) 仅使用配对数据，在该空间中通过1-Wasserstein距离进行联合分布匹配。该两阶段方法最小化了联合分布间1-Wasserstein距离的上界，降低对稀缺配对样本的依赖，同时支持快速单步生成。理论上，我们建立了非渐近误差界，并证明未配对数据的关键优势：提升生成结果的几何保真度。进一步地，通过扩展两个核心步骤，LSDM提供了一个连贯的统计视角，关联广泛潜在空间方法。值得注意的是，潜在扩散模型（LDMs）可视为LSDM的一种变体，其通过得分匹配间接实现联合分布匹配。因此，我们的结果也为LDMs的一致性提供了理论洞察。在真实图像任务（包括类别条件生成与图像超分辨率）上的实证评估表明，LSDM能有效利用未配对数据提升生成质量。
原文摘要 · Abstract (English)
We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and unpaired data, and (ii) performing joint distribution matching in this space via the 1-Wasserstein distance, using only paired data. This two-step approach minimizes an upper bound on the 1-Wasserstein distance between joint distributions, reducing reliance on scarce paired samples while enabling fast one-step generation. Theoretically, we establish non-asymptotic error bounds and demonstrate a key benefit of unpaired data: enhanced geometric fidelity in generated outputs. Furthermore, by extending the scope of its two core steps, LSDM provides a coherent statistical perspective that connects to a broad class of latent-space approaches. Notably, Latent Diffusion Models (LDMs) can be viewed as a variant of LSDM, in which joint distribution matching is achieved indirectly via score matching. Consequently, our results also provide theoretical insights into the consistency of LDMs. Empirical evaluations on real-world image tasks, including class-conditional generation and image super-resolution, demonstrate the effectiveness of LSDM in leveraging unpaired data to enhance generation quality.
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