State of health is a critical state which evaluates the degradation level of batteries. However, it cannot be measured directly but requires estimation. While accurate state of health estimation has progressed markedly, the time- and resource-consuming degradation experiments to generate target battery labels hinder the development of state of health estimation methods. In this article, we design a deep-learning framework to enable the estimation of battery state of health in the absence of target battery labels. This framework integrates a swarm of deep neural networks equipped with domain adaptation to produce accurate estimation. We employ 65 commercial batteries from 5 different manufacturers to generate 71,588 samples for cross-validation. The validation results indicate that the proposed framework can ensure absolute errors of less than 3% for 89.4% of samples (less than 5% for 98.9% of samples), with a maximum absolute error of less than 8.87% in the absence of target labels. This work emphasizes the power of deep learning in precluding degradation experiments and highlights the promise of rapid development of battery management algorithms for new-generation batteries using only previous experimental data.