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I have a lack of understanding about this issue. Could anybody explain it or give an advice to a good literature regarding it? I don't understand what is a explicit density model and how it differs from an implicit density one. Could anyone exemplify the difference between these two kinds of models?

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Here is the picture source.

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This paragraph in this paper may be of help, methinks.

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The main difference between explicit density models and implicit density models is that explicit density models, use an explicit density function and implicit density models don't. In other words explicit models assume some prior distribution about the data. For example the work of Dinh et. al., which in the reference link is classified as an explicit model, use an isotropic unit norm Gaussian as the prior (page 7, of the above link). One example of implicit density model is the work of Bengio et. al, also mentioned in the reference link, to estimate the distribution of the data they learn the transition operator of a Markov chain whose stationary distribution estimates the data distribution.

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