We introduce Conditional Push-Forward Neural Networks (CPFN), a generative framework for estimating conditional distributions. Instead of directly modeling the conditional density, the method learns a stochastic transformation that, starting from a suitably chosen latent random vector, produces samples that approximately follow the same distribution as the observed data given a certain input. This approach enables efficient conditional sampling and straightforward estimation of conditional statistics via Monte Carlo methods. The model is trained using an objective function derived from the Kullback-Leibler divergence, without requiring invertibility or adversarial training. We also establish a near-asymptotic consistency result and demonstrate experimentally that CPFN can achieve performance comparable to, or even better than, state-of-the-art methods, including kernel estimators, tree-based algorithms, and popular deep learning techniques, while remaining lightweight and easy to train.