  Score-based diffusion models have emerged as one of the most promising
frameworks for deep generative modelling. In this work we conduct a systematic
comparison and theoretical analysis of different approaches to learning
conditional probability distributions with score-based diffusion models. In
particular, we prove results which provide a theoretical justification for one
of the most successful estimators of the conditional score. Moreover, we
introduce a multi-speed diffusion framework, which leads to a new estimator for
the conditional score, performing on par with previous state-of-the-art
approaches. Our theoretical and experimental findings are accompanied by an
open source library MSDiff which allows for application and further research of
multi-speed diffusion models.

Machine Learning;Computer Vision and Pattern Recognition;Machine Learning