This work ddresses challenges in Continuous Conditional Generative Modeling (CCGM) by proposing Continuous Conditional Diffusion Models (CCDM), tailored to overcome limitations encountered with existing Conditional Diffusion Models (CDMs). CCGM aims to estimate the distribution of high-dimensional data, such as images, conditioned on scalar continuous variables known as regression labels.

CCDMs are introduced as the first diffusion-based models explicitly designed for the CCGM task, aiming to enhance the stability of model training and improve the quality of generated images. The key innovations of CCDMs include conditional forward and reverse diffusion processes, which consider regression labels during generation, and a modified denoising U-Net architecture customized for regression labels.

Existing CDMs face challenges in integrating with CCGM due to issues such as inadequate U-Net architectures and difficulties in handling regression labels during model fitting. CCDMs address these challenges by introducing specially designed diffusion processes that consider regression labels and incorporating a modified denoising U-Net architecture with a custom conditioning mechanism.