# Local Differential Privacy Image Generation Using Flow-Based Deep Generative Models
## 5 Discussion  
We showed an algorithm (DP-GLOW) for generating useful images for diagnosis and medical AI, while \(\epsilon\)-LDP is guaranteed against any image in the training distribution. Furthermore, this is the first study to apply an \(\epsilon\)-LDP algorithm against a medical image itself. Additionally, we validated the usefulness of the \(\epsilon\)-LDP CXR images generated by AI for pneumonia detection: we showed the AUC as a function of the privacy budget. Finally, this is the first work to adopt flow-based DGMs for LDP processing.  
For DP-GLOW, the AUCs for pneumonia detection significantly change from 0.539 to 0.807, while the privacy budget varies from \(10^{1}\cdot H\cdot W(=2,621,440)\) to \(\infty\). This means that this range of the privacy budget is indeed meaningful, whereas the privacy budget is very large compared with usual values of \(\epsilon\)-LDP for scalar quantities. This finding implies that we must normalize the privacy budget so that we can consistently handle \(\epsilon\)-LDP for vector quantities. To normalize the budget, we compute the privacy budgets per image pixel. To this end, we intentionally indicated the privacy budget to have a common factor \(H\cdot W\). Therefore, the actual privacy budgets per image pixel in this study are from \(10^{1}\) to \(\infty\), which are not much larger than commonly accepted privacy budgets.  
Most of the approximate forms in CXR images are preserved and privacy is not protected with the image domain LDP. On the other hand, given a low privacy budget, DP-GLOW deforms the image so much that individuals cannot be identified. However, the AUCs for pneumonia detection are similar with the low privacy budget between DP-GLOW and the image domain LDP.  
This study has several future directions. First, we adopted CXR images but one can adopt other kinds of image including nonmedical images. Second, we can readily extend this method to three-dimensional (3D) flow-based DGMs to generate \(\epsilon\)-LDP 3D images, such as CT (Computed Tomography) and MR (Magnetic Resonance) images. Third, we can use other flow-based DGMs different from GLOW. Fourth, although we have formulated our LDP algorithm using flow-based deep generative models, we are now attempting to adapt it for denoising diffusion probabilistic models [18].  
This study has a limitation--we must train GLOW with many medical images to generate \(\epsilon\)-LDP-processed medical images using DP-GLOW. The training is very difficult when medical images of interest are not available. However, once the GLOW is trained with the medical images of interest, we can distribute the GLOW model to further release medical images of the same kind to the public using DP-GLOW. Empirically, we know that at least 1000 images are needed to train the GLOW model satisfactorily. However, the number of images required may vary if we use a different flow-based deep generative model. Additionally, due to memory limitations, it is expected that we cannot process large-sized 3D images. Furthermore, DP-GLOW cannot handle medical images with varying resolutions.