Semi-Supervised Generative Learning via Latent Space Distribution Matching

Conditional diffusion models have become a powerful and flexible framework for learning complex conditional distributions from labeled data. In practice, however, acquiring high-quality labels is costly and time-consuming, leaving large volumes of unlabeled data unused. To address this, we introduce label-augmented conditional diffusion (LACD), a simple and effective approach that incorporates unlabeled examples by assigning them a designated trivial label and performing joint denoising score matching over the augmented dataset. We provide sufficient conditions guaranteeing population-level identifiability of the target conditional distribution under this scheme. Moreover, we establish rigorous statistical guarantees: when sufficiently many unlabeled samples are available, the sampling distribution produced by LACD converges strictly faster than the purely supervised estimator in total variation distance, and at least as fast in Wasserstein-1 distance. Extensive experiments on synthetic, image, and tabular benchmarks corroborate our theory and show substantial gains in sample efficiency and generative performance compared with the purely supervised estimator.

Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.

Generative modeling and self-supervised representation learning (SSL) optimize structurally different objectives: generative training rewards distributional fidelity, while SSL rewards semantic coherence. Yet recent work repeatedly finds that SSL features improve generative training, though the mechanism of this synergy remains unclear. Here, we study the benefits of SSL in generative modeling in the framework of one-step generation where the role of representation is explicit: frozen SSL features are used to match generated samples to real data. We use the Sinkhorn divergence in that feature space, providing a tractable surrogate for the Wasserstein distance, the population-level discrepancy approximated by Fréchet-style evaluation metrics (such as FID). We find that this objective becomes highly effective when computed in a semantically structured SSL feature space (a 39$\times$ reduction in ImageNet FID). We trace this behavior primarily to matching estimation: semantic SSL features that suppress nuisance reconstruction details induce a more compact geometry, making distribution matching more tractable. As a consequence, the best training SSL features need not match the features used by the evaluation metric. In particular, we show that using Inception as the feature extractor can improve FID while degrading matching stability and sample quality, revealing a form of metric hacking. Using extensive experiments on ImageNet, we identify which SSL feature families lead to best generation performance and show that matching stability is a quantitative criterion for selecting them. Code is available at https://github.com/Genentech/semantic-transport-generation.