Beyond Diagonal Covariance: Flexible Posterior VAEs via Free-Form Injective Flows
This work addresses a bottleneck in variational autoencoders for researchers and practitioners in generative modeling, offering a more flexible posterior without increased computational overhead.
The paper tackled the limited representational capacity of diagonal covariance VAEs by proposing a regularized free-form injective flow variant, which achieves a full Gaussian covariance posterior with comparable computational cost, resulting in improved model likelihood on image datasets.
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.