# Semi-Supervised Generative Learning via Latent Space Distribution Matching

arXiv: https://arxiv.org/abs/2603.04223 · HTML: https://mlsanity.com/paper/2603.04223/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations](https://mlsanity.com/paper/2607.16725/) (2026)

## Abstract (arXiv)

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.