# Semi-Supervised Conditional Diffusion via Label Augmentation

arXiv: https://arxiv.org/abs/2607.16685 · HTML: https://mlsanity.com/paper/2607.16685/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 34 of its 63 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Medical Image Synthesis for Data Augmentation and Anonymization using Generative Adversarial Networks](https://mlsanity.com/paper/1807.10225/) (2018)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [Few-Shot Diffusion Models](https://mlsanity.com/paper/2205.15463/) (2022)
- [Diffusion Models and Semi-Supervised Learners Benefit Mutually with Few Labels](https://mlsanity.com/paper/2302.10586/) (2023)
- [Efficient and Adaptive Linear Regression in Semi-Supervised Settings](https://mlsanity.com/paper/1701.04889/) (2017)
- [Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes](https://mlsanity.com/paper/2412.04140/) (2024)
- [Wasserstein Generative Regression](https://mlsanity.com/paper/2306.15163/) (2023)
- [Counterfactual Generative Modeling with Variational Causal Inference](https://mlsanity.com/paper/2410.12730/) (2024)
- [Optimal and Safe Estimation for High-Dimensional Semi-Supervised Learning](https://mlsanity.com/paper/2011.14185/) (2020)
- [Conditional Data Synthesis Augmentation](https://mlsanity.com/paper/2504.07426/) (2025)
- [Enhancing Accuracy in Generative Models via Knowledge Transfer](https://mlsanity.com/paper/2405.16837/) (2024)

## Abstract (arXiv)

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.