用灵活的流模型提升VAE后验表达能力，效果更好且计算不增。
Beyond Diagonal Covariance: Flexible Posterior VAEs via Free-Form Injective Flows
- 引入自由形式注入流改进后验分布，突破对角协方差限制。
- 在图像数据上显著提升模型似然，达到全协方差水平。
- 适合需要高精度不确定性建模的研究者使用。
变分自编码器（VAEs）是强大的生成模型，广泛用于学习可解释的潜在空间、量化不确定性及压缩数据。传统VAE受限于计算开销，通常采用对角协方差后验分布。基于微分几何分析，我们揭示了对角协方差VAE在表示能力上的固有局限性，通过低维示例予以说明。为此，我们提出一种正则化版本的自由形式注入流（Free-form Injective Flow, FIF），可视为具备高度灵活、隐式定义后验的VAE。关键在于，该正则化使后验等价于全协方差高斯分布，同时保持与标准对角协方差VAE相当的计算成本。在图像数据集上的实验验证了该方法的有效性，表明引入全协方差能显著提升模型似然性能。
原文摘要 · Abstract (English)
Variational Autoencoders (VAEs) are powerful generative models widely used for learning interpretable latent spaces, quantifying uncertainty, and compressing data for downstream generative tasks. VAEs typically rely on diagonal Gaussian posteriors due to computational constraints. Using arguments grounded in differential geometry, we demonstrate inherent limitations in the representational capacity of diagonal covariance VAEs, as illustrated by explicit low-dimensional examples. In response, we show that a regularized variant of the recently introduced Free-form Injective Flow (FIF) can be interpreted as a VAE featuring a highly flexible, implicitly defined posterior. Crucially, this regularization yields a posterior equivalent to a full Gaussian covariance distribution, yet maintains computational costs comparable to standard diagonal covariance VAEs. Experiments on image datasets validate our approach, demonstrating that incorporating full covariance substantially improves model likelihood.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。