The reconstruction loss and the Kullback-Leibler divergence (KLD) loss in a variational autoencoder (VAE) often play antagonistic roles, and tuning the weight of the KLD loss in $\beta$-VAE to achieve a balance between the two losses is a tricky and dataset-specific task. As a result, current practices in VAE training often result in a trade-off between the reconstruction fidelity and the continuity$/$disentanglement of the latent space, if the weight $\beta$ is not carefully tuned. In this paper, we present intuitions and a careful analysis of the antagonistic mechanism of the two losses, and propose, based on the insights, a simple yet effective two-stage method for training a VAE. Specifically, the method aggregates a learned Gaussian posterior $z \sim q_{\theta} (z|x)$ with a decoder decoupled from the KLD loss, which is trained to learn a new conditional distribution $p_{\phi} (x|z)$ of the input data $x$. Experimentally, we show that the aggregated VAE maximally satisfies the Gaussian assumption about the latent space, while still achieves a reconstruction error comparable to when the latent space is only loosely regularized by $\mathcal{N}(\mathbf{0},I)$. The proposed approach does not require hyperparameter (i.e., the KLD weight $\beta$) tuning given a specific dataset as required in common VAE training practices. We evaluate the method using a medical dataset intended for 3D skull reconstruction and shape completion, and the results indicate promising generative capabilities of the VAE trained using the proposed method. Besides, through guided manipulation of the latent variables, we establish a connection between existing autoencoder (AE)-based approaches and generative approaches, such as VAE, for the shape completion problem. Codes and pre-trained weights are available at https://github.com/Jianningli/skullVAE

翻译：重建损耗和变换自动coder (VAE) 中Kullback- Leiber 损耗(KLD) 变换自动coder (VAE) 中,重建损耗和 Kullback- Leiber 损益(KLD) 损耗往往起到对抗作用,调整KLD损失的重量($\beeta$-VAE) 以在两个损失之间取得平衡是一项棘手而具体的数据组合任务。因此,VAE培训中目前的做法往往导致重建忠诚与潜在空间的连续性(美元/美元) 的偏差。如果变换不小心调整权重 $\beta(VA) 对两种损失的对抗机制进行直觉分析并进行仔细分析,根据洞察,简单而有效的两阶段方法用于培训VAEEE。这个方法将Gaussial 的变现变现的变现方法(WLD) 和变现的变现的变现法作为变现法。