Drift Variation Autoencoder: Unifying Generation and Representation Learning through Conditional Posterior Flow Matching

Stochastic masking, cropping, or modality removal makes deterministic reconstruction an incomplete target: one observation can admit many clean completions. This work takes the corresponding posterior P(Xmid C) as the common statistical object for conditional generation and generatively sufficient representation learning. Drift Variation autoencoder trains a masked encoder Z=E(C) and a conditional flow decoder with one clean-prediction Flow Matching loss. The analysis first decomposes the ideal conditional KL into generator approximation and the representation deficiency I(X;Cmid Z). It then derives orthogonal risk decompositions for conditional Flow Matching. For an affine Gaussian path, the clean-prediction representation gap is zero if and only if P(Xmid Z)=P(Xmid C). Thus the encoder-dependent excess clean-prediction risk induced by Flow Matching and the profiled ideal conditional KL have the same posterior-sufficient zero set, without being numerically equal objectives. An exact conditional field with a zero-noise endpoint then generates P(Xmid Z) and hence P(Xmid C) at a joint ideal optimum. The result extends to continuous multimodal product spaces when the complete modality tuple remains the Flow target for every observation mask. On CrossGeom-4, an 18-run controlled benchmark, observable factors have linear-probe R2 of 0.9990-0.9992, shuffling the joint model's encoder condition increases conditional error by 13.5×-15.7×, and joint target attention reduces disagreement on an unobserved factor shared by two outputs by 90.1-92.8% relative to independent target decoders. Visible modalities are also generated and reconstructed, directly validating the full-tuple objective. Unconditional mode balance remains imperfect, delimiting the empirical claim to a controlled multimodal proof of concept.