New Autoencoder Unifies Generation and Representation Learning

Traditional deterministic reconstruction methods struggle when a single observation can lead to multiple valid completions, especially with stochastic data corruption like masking or cropping. This paper proposes the Drift Variation Autoencoder (DVAE), which addresses this by focusing on the conditional posterior probability of data given its context. The DVAE employs a masked encoder to generate latent representations and a conditional flow decoder, trained with a unique clean-prediction Flow Matching loss. The theoretical analysis of DVAE shows how it decomposes the ideal conditional KL divergence and derives orthogonal risk decompositions for Flow Matching. Crucially, it demonstrates that the representation gap for clean-prediction is zero if the model accurately captures the conditional data distribution. Empirical validation on a controlled multimodal benchmark, CrossGeom-4, shows significant improvements in linear-probe R^2 for observable factors and substantial reductions in disagreement for unobserved factors, validating its full-tuple objective.