Liquid storage tanks play a vital role in the modern chemical process industry (CPI). The strong ground motion caused by large-scale earthquakes may easily impose severe structural damage on liquid storage tanks, leading to a series of catastrophic cascaded events. The seismic damage estimation of liquid storage tanks is a challenging problem, as the fluid-structure interaction exhibits extremely complicated and non-stationary response behavior. This study develops a novel data-driven methodology to estimate the seismic damage state probability distribution of liquid storage tanks in the contexts of label ambiguity and data imbalance. With the support of the advanced deep learning framework, synthetic oversampling methods, and label enhancement techniques, a hybrid deep belief network-based label distribution learning system (HDBN-LDLS) is proposed for probability distribution learning. The proposed HDBN-LDLS is evaluated on the widely used ALA database. Simulation results indicate that HDBN-LDLS can achieve a balanced estimation for all damage states while maintaining sufficient robustness to cope with label ambiguity. The reliability of the obtained data-driven model is validated by a damaged tank in the 2006 Silakhor earthquake. For practical applications, a more natural way to estimate a seismic damaged tank is to assign a membership degree to each possible damage state. The proposed methodology can quickly obtain the seismic damage state probability curves of a specific liquid storage tank, which can be used to support quantitative risk assessment and seismic design.