Now we have all the ingredients required to sample data points of the estimated distribution $Q_{X , Y}$ with the generative model by proceeding as follow:

1. Draw $\{(n_{X,j}, n_{Y,j})\}_{j=1}^n$ , n samples independent and identically distributed from the joint distribution $Q_{N_X}(\theta_{N_X})\times Q_{N_Y}(\theta_{N_Y})$ of independent noise variables $( N_X , N_Y )$.
2. Generate n samples $\hat{\mathcal{D}} = \{(\hat{x}_j, \hat{y}_j) \}_{j=1}^n$, where each estimated sample $\hat{x}_j$ of variable $X$ is computed from $\hat{f}_X(\theta_X)$ with the j-th estimated samples $n_{X , j}$; then each estimated sample $\hat{y}_j$ of variable $Y$ is computed from $\hat{f}_Y(\theta_Y)$ with the j-th estimated samples $n_{Y , j}$ and $\hat{x}_j$.

Generative candidate models supports both interventions and counterfactual reasoning.