The Normalizing Flow (NF) models a general probability density by estimating
an invertible transformation applied on samples drawn from a known
distribution. We introduce a new type of NF, called Deep Diffeomorphic
Normalizing Flow (DDNF). A diffeomorphic flow is an invertible function where
both the function and its inverse are smooth. We construct the flow using an
ordinary differential equation (ODE) governed by a time-varying smooth vector
field. We use a neural network to parametrize the smooth vector field and a
recursive neural network (RNN) for approximating the solution of the ODE. Each
cell in the RNN is a residual network implementing one Euler integration step.
The architecture of our flow enables efficient likelihood evaluation,
straightforward flow inversion, and results in highly flexible density
estimation. An end-to-end trained DDNF achieves competitive results with
state-of-the-art methods on a suite of density estimation and variational
inference tasks. Finally, our method brings concepts from Riemannian geometry
that, we believe, can open a new research direction for neural density
estimation.

DDNF 模型是一种基于普通微分方程 (ODE) 和递归神经网络 (RNN) 的正则差分流模型，具有高效的似然度评估和柔性的密度估计能力， 是一种具有竞争力的新型神经密度估计技术，还可以在 Riemannian 半群中扩展。