transformation must be carefully designed to be invertible and to have a tractable Jacobian and in fact a tractable determinant of the Jacobian in particular this requirement says that the latent variables must have the same dimension allottee as the data space so if we want to generate 3,000 pixels we need to have 3,000 latent variables it makes it harder to design the model to have exactly the capacity that we would like to have another major family of models is those that have intractable density functions but then use tractable