Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations
Changyu Liu, Yuling Jiao, Jian Huang
stat.ML, cs.LG
Submitted: 2026-07-18
Comments: 35 pages, 4 figures and 1 table
License: http://creativecommons.org/licenses/by/4.0/
The gist: Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant.
Terminology
Abstract
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.
Sources
- Semi-Supervised Generative Learning via Latent Space Distribution Matching
- Conditional Stochastic Interpolation for Generative Learning
- Latent Schr{\"o}dinger Bridge Diffusion Model for Generative Learning
- Convergence Analysis of Flow Matching in Latent Space with Transformers
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