The Variational Autoencoder (VAE) is a seminal approach in deep generative modeling with latent variables. Interpreting its reconstruction process as a nonlinear transformation of samples from the latent posterior distribution, we apply the Unscented Transform (UT) -- a well-known distribution approximation used in the Unscented Kalman Filter (UKF) from the field of filtering. A finite set of statistics called sigma points, sampled deterministically, provides a more informative and lower-variance posterior representation than the ubiquitous noise-scaling of the reparameterization trick, while ensuring higher-quality reconstruction. We further boost the performance by replacing the Kullback-Leibler (KL) divergence with the Wasserstein distribution metric that allows for a sharper posterior. Inspired by the two components, we derive a novel, deterministic-sampling flavor of the VAE, the Unscented Autoencoder (UAE), trained purely with regularization-like terms on the per-sample posterior. We empirically show competitive performance in Fr\'echet Inception Distance (FID) scores over closely-related models, in addition to a lower training variance than the VAE.

翻译：变分自编码器（VAE）是深度生成模型中引入潜变量的开创性方法。通过将其重建过程解释为对潜变量后验分布样本的非线性变换，我们引入了无迹变换（UT）——一种在滤波领域（如无迹卡尔曼滤波器（UKF））中广泛使用的分布近似方法。通过确定性采样得到的有限统计量（即σ点）能够提供比重参数化技巧中常见的噪声缩放方法更丰富、方差更低的后验表示，同时确保更高质量的重建。我们进一步用Wasserstein分布度量替代Kullback-Leibler（KL）散度，以支持更尖锐的后验分布，从而提升模型性能。受这两个组成部分启发，我们提出了一种新颖的确定性采样变体VAE——无迹自编码器（UAE），其训练仅依赖于每个样本后验上的正则化项。实验表明，与紧密相关的模型相比，UAE在Fréchet Inception Distance（FID）评分上具有竞争力的表现，同时训练方差低于标准VAE。