# CCDM: Continuous Conditional Diffusion Models for Image Generation

arXiv: https://arxiv.org/abs/2405.03546 · HTML: https://mlsanity.com/paper/2405.03546/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 39 of its 61 references that are in the map.
- First posted on arXiv 6 May 2024.

## Placed in

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

## Builds on (most cited first, 30 of 39)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Differentiable Augmentation for Data-Efficient GAN Training](https://mlsanity.com/paper/2006.10738/) (2020)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Geometric GAN](https://mlsanity.com/paper/1705.02894/) (2017)
- [Rebooting ACGAN: Auxiliary Classifier GANs with Stable Training](https://mlsanity.com/paper/2111.01118/) (2021)
- [DiffFashion: Reference-based Fashion Design with Structure-aware Transfer by Diffusion Models](https://mlsanity.com/paper/2302.06826/) (2023)
- [PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network For Inverse Design](https://mlsanity.com/paper/2106.03620/) (2021)

## Built on by (most cited first, 8 of 8)

- [UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2502.05749/) (2025)
- [A Unified and Fast-Sampling Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2505.21528/) (2025)
- [Imbalance-Robust and Sampling-Efficient Continuous Conditional GANs via Adaptive Vicinal Learning and Auxiliary Regularization](https://mlsanity.com/paper/2508.01725/) (2025)
- [LocaGen: Low-Overhead Indoor Localization Through Spatial Augmentation](https://mlsanity.com/paper/2511.18158/) (2025)
- [Breaking the Bottlenecks: Scalable Diffusion Models for 3D Molecular Generation](https://mlsanity.com/paper/2601.08963/) (2026)
- [Enhancing Diffusion-Based Quantitatively Controllable Image Generation via Matrix-Form EDM and Adaptive Vicinal Training](https://mlsanity.com/paper/2602.02114/) (2026)
- [Explainable Pathomics Feature Visualization via Correlation-aware Conditional Feature Editing](https://mlsanity.com/paper/2602.05397/) (2026)
- [From Characterization To Construction: Generative Quantum Circuit Synthesis from Gate Set Tomography Data](https://mlsanity.com/paper/2605.01367/) (2026)

## Abstract (arXiv)

Continuous Conditional Generative Modeling (CCGM) estimates high-dimensional data distributions, such as images, conditioned on scalar continuous variables (aka regression labels). While Continuous Conditional Generative Adversarial Networks (CcGANs) were designed for this task, their instability during adversarial learning often leads to suboptimal results. Conditional Diffusion Models (CDMs) offer a promising alternative, generating more realistic images, but their diffusion processes, label conditioning, and model fitting procedures are either not optimized for or incompatible with CCGM, making it difficult to integrate CcGANs' vicinal approach. To address these issues, we introduce Continuous Conditional Diffusion Models (CCDMs), the first CDM specifically tailored for CCGM. CCDMs address existing limitations with specially designed conditional diffusion processes, a novel hard vicinal image denoising loss, a customized label embedding method, and efficient conditional sampling procedures. Through comprehensive experiments on four datasets with resolutions ranging from 64x64 to 192x192, we demonstrate that CCDMs outperform state-of-the-art CCGM models, establishing a new benchmark. Ablation studies further validate the model design and implementation, highlighting that some widely used CDM implementations are ineffective for the CCGM task. Our code is publicly available at https://github.com/UBCDingXin/CCDM.