By introducing a frequency dependence source prior including full-band and clique models, independent vector analysis (IVA) has been successfully used for convolutive blind source separation (BSS). In addition, independent low-rank matrix analysis (ILRMA) learns a low-rank approximation of the timefrequency structure of source signals. This paper presents IVA using a clique-based frequency dependence model with time-varying clique variances to combine advantages of both ILRMA and clique-model-based IVA for BSS of speech signals. Although conventional clique models are effective in separating sources with specific spectral structures, the dependency among the cliques is considered by overlaps between cliques or a global clique of all frequency bins if there is. To avoid the permutation problem by strengthening the dependency among the cliques, we develop a generalized probability-density-function (pdf) model imposing a variable exponent on the summed cliques with overlaps and time-varying clique variances, which may include most conventional source models as particular cases. In addition, update rules of the clique variances and demixing matrices are derived by minimization of the cost function of BSS as well as non-negative matrix factorization (NMF) and auxiliary function techniques for fast and robust convergence, respectively. Through experiments on BSS of speech mixtures with various mixing conditions, the proposed IVA showed improved separation performance than the conventional methods. Experimental results consistently demonstrated that the performance of a method could be determined in general by the trade-off between the degree of freedom of source models (as long as model parameters were accurately estimated) and the vulnerability to the permutation problem. INDEX TERMS Blind source separation, clique, independent vector analysis, time-varying variance.