Paper:
Autoencoder reconstructions are widely used for the task of unsupervised anomaly localization. Indeed, an autoencoder trained on normal data is expected to only be able to reconstruct normal features of the data, allowing the segmentation of anomalous pixels in an image via a simple comparison between the image and its autoencoder reconstruction. In practice however, local defects added to a normal image can deteriorate the whole reconstruction, making this segmentation challenging. To tackle the issue, we propose in this paper a new approach for projecting anomalous data on a autoencoder-learned normal data manifold, by using gradient descent on an energy derived from the autoencoder's loss function. This energy can be augmented with regularization terms that model priors on what constitutes the user-defined optimal projection. By iteratively updating the input of the autoencoder, we bypass the loss of high-frequency information caused by the autoencoder bottleneck. This allows to produce images of higher quality than classic reconstructions. Our method achieves state-of-the-art results on various anomaly localization datasets. It also shows promising results at an inpainting task on the CelebA dataset.

Review:
Summary: The paper proposes to use autoencoder for anomaly localization. The approach learns to project anomalous data on an autoencoder-learned manifold by using gradient descent on energy derived from the autoencoder's loss function. The proposed method is evaluated using the anomaly-localization dataset (Bergmann et al. CVPR 2019) and qualitatively for the task of image inpainting task on CelebA dataset.
Pros: 
+ surprisingly simple approach that led to significantly better results. 
+ applications to image inpainting, and demonstrates better visual results than using simple VAE.
Concern :
- While I agree that authors have shown relative performance compared to various approaches,  I am not able to map the results of Table-1 to that of Table-3 (second column ROC values) in Bergmann et al. CVPR'19. The setup in two works seem similar. Can the authors please comment to help me understand this difference?
- The proposed approach leads to better performance over the baseline models; it is not clear what is a suitable baseline model for the problem of anomaly localization is?
- The results for image inpainting looks promising. The authors may want to add comparison with existing image inpainting approaches for the reader to better appreciate the proposed approach.