  Unsupervised disentanglement learning is a crucial issue for understanding
and exploiting deep generative models. Recently, SeFa tries to find latent
disentangled directions by performing SVD on the first projection of a
pre-trained GAN. However, it is only applied to the first layer and works in a
post-processing way. Hessian Penalty minimizes the off-diagonal entries of the
output's Hessian matrix to facilitate disentanglement, and can be applied to
multi-layers.However, it constrains each entry of output independently, making
it not sufficient in disentangling the latent directions (e.g., shape, size,
rotation, etc.) of spatially correlated variations. In this paper, we propose a
simple Orthogonal Jacobian Regularization (OroJaR) to encourage deep generative
model to learn disentangled representations. It simply encourages the variation
of output caused by perturbations on different latent dimensions to be
orthogonal, and the Jacobian with respect to the input is calculated to
represent this variation. We show that our OroJaR also encourages the output's
Hessian matrix to be diagonal in an indirect manner. In contrast to the Hessian
Penalty, our OroJaR constrains the output in a holistic way, making it very
effective in disentangling latent dimensions corresponding to spatially
correlated variations. Quantitative and qualitative experimental results show
that our method is effective in disentangled and controllable image generation,
and performs favorably against the state-of-the-art methods. Our code is
available at https://github.com/csyxwei/OroJaR
