Counterfactual  models  aim  at  explaining  machine  learning predictions by answering questions of the form "had  the  input  been different,  would  the  output have been the same?" The literature mostly focused on two divergent frameworks to build these models:  the neareast  counterfactual  instance principle –which is oblivious of the latent statistical distributions, and Pearl’s causal reasoning –which relies on a model unknown in practice.  We extend a recent work that substituted causal interventions by a push-forward operator between probability distributions.  We show that this approach leads to statistically consistent counterfactual explanations, free of prior assumptions on the data generation process.