Orthogonal Jacobian Regularization for Unsupervised Disentanglement in Image Generation

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 pretrained 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.