Danilo Jimenez Rezende

Danilo Jimenez Rezende coauthored the 2014 stochastic-backpropagation work with Shakir Mohamed and Daan Wierstra, developing trainable generative and approximate-inference models.^[ref] With Shakir Mohamed, he subsequently developed normalizing flows for richer approximations in variational inference.^[ref]

An original one-dimensional transformation illustrates the density accounting. Let $ϵ$ have standard normal distribution and take $Z=2ϵ+1$. Sampling is straightforward, but its density must also account for the stretching of length:At $z=1$, this is $1/(2\sqrt{2\pi })$. The factor $1/2$ comes from the absolute derivative of the inverse affine map. Omitting it would give a density integrating to $2$ instead of $1$.

The example is only an affine Gaussian transformation; it does not claim that every nonlinear transformation preserves a Gaussian family. A normalizing flow composes suitable invertible transformations while tracking the corresponding density changes. This connects an efficient sampling procedure to the density evaluation needed in a variational objective, rather than treating the generated samples alone as a complete inference method.