We address a challenging problem-modeling high-dimensional, long-range dependencies between nonnormal multivariates, which is important for demanding applications such as cross-market modeling (CMM). With heterogeneous indicators and markets, CMM aims to capture between-market financial couplings and influence over time and within-market interactions between financial variables. We make the first attempt to integrate deep variational sequential learning with copula-based statistical dependence modeling and characterize both temporal dependence degrees and structures between hidden variables representing nonnormal multivariates. Our copula variational learning network weighted partial regular vine copula-based variational long short-term memory (WPVC-VLSTM) integrates variational long short-term memory (LSTM) networks and regular vine copula to model variational sequential dependence degrees and structures. The regular vine copula models nonnormal distributional dependence degrees and structures. VLSTM captures variational long-range dependencies coupling high-dimensional dynamic hidden variables without strong hypotheses and multivariate constraints. WPVC-VLSTM outperforms benchmarks, including linear models, stochastic volatility models, deep neural networks, and variational recurrent networks in terms of both technical significance and portfolio forecasting performance. WPVC-VLSTM shows a step-forward for CMM and deep variational learning.