Conditional sampling of variational autoencoders (VAEs) is needed in various applications, such as missing data imputation, but is computationally intractable. A principled choice for asymptotically exact conditional sampling is Metropolis-within-Gibbs (MWG). However, we observe that the tendency of VAEs to learn a structured latent space, a commonly desired property, can cause the MWG sampler to get "stuck" far from the target distribution. This paper mitigates the limitations of MWG: we systematically outline the pitfalls in the context of VAEs, propose two original methods that address these pitfalls, and demonstrate an improved performance of the proposed methods on a set of sampling tasks.

翻译：变分自编码器（VAE）的条件采样在许多应用中必不可少，例如缺失数据插补，但其计算复杂度较高。从理论上讲，实现渐近精确条件采样的一个合理选择是吉布斯采样器内部的Metropolis算法。然而，我们观察到，VAE倾向于学习结构化的隐空间（这一特性通常被认为是理想属性），这种倾向可能导致Metropolis-within-Gibbs采样器在远离目标分布的区域陷入停滞。本文旨在缓解Metropolis-within-Gibbs采样器的局限性：我们系统性地阐述了VAE在该方法中存在的隐患，提出了两种解决这些隐患的原创方法，并通过一组采样任务验证了所提方法性能的提升。