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）的条件采样在多种应用（如缺失数据插补）中不可或缺，但计算上难以实现。渐近精确条件采样的一种理论依据是吉布斯采样中的Metropolis算法（Metropolis-within-Gibbs, MWG）。然而，我们观察到，VAE倾向于学习结构化潜空间这一常见特性，可能导致MWG采样器远离目标分布而陷入“停滞”。本文旨在缓解MWG的局限性：系统性地阐述了VAE条件下的陷阱，提出了两种解决这些陷阱的新方法，并在多个采样任务中证明了所提方法具有更优性能。