This book constitutes the refereed proceedings of the First MICCAI Workshop on Deep Generative Models, DG4MICCAI 2021, and the First MICCAI Workshop on Data Augmentation, Labelling, and Imperfections, DALI 2021, held in conjunction with MICCAI 2021, in October 2021. The workshops were planned to take place in Strasbourg, France, but were held virtually due to the COVID-19 pandemic. DG4MICCAI 2021 accepted 12 papers from the 17 submissions received. The workshop focusses on recent algorithmic developments, new results, and promising future directions in Deep Generative Models. Deep generative models such as Generative Adversarial Network (GAN) and Variational Auto-Encoder (VAE) are currently receiving widespread attention from not only the computer vision and machine learning communities, but also in the MIC and CAI community. For DALI 2021, 15 papers from 32 submissions were accepted for publication. They focus on rigorous study of medical data related to machine learning systems.