A network to transform/predict one probability distribution to another

Question

I have a random variable of a particular density (e.g., normal), and a known probability distribution (e.g., mixture Gaussian). I used a simple KL measure to predict/transform one another. Now I need to use a neural network to perform such task, and transform one random variable to another. Can you suggest a type of network to perform that, if there is an open source code would be very helpful.