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

arXiv: https://arxiv.org/abs/2608.25138 · HTML: https://mlsanity.com/paper/2608.25138/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Transfusion: Predict the Next Token and Diffuse Images with One Multi-Modal Model](https://mlsanity.com/paper/2408.11039/) (2024)
- [Janus: Decoupling Visual Encoding for Unified Multimodal Understanding and Generation](https://mlsanity.com/paper/2410.13848/) (2024)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [MultiMAE: Multi-modal Multi-task Masked Autoencoders](https://mlsanity.com/paper/2204.01678/) (2022)
- [Denoising Diffusion Autoencoders are Unified Self-supervised Learners](https://mlsanity.com/paper/2303.09769/) (2023)
- [4M: Massively Multimodal Masked Modeling](https://mlsanity.com/paper/2312.06647/) (2023)
- [Diffusion-Based Representation Learning](https://mlsanity.com/paper/2105.14257/) (2021)
- [Self-Supervised Flow Matching for Scalable Multi-Modal Synthesis](https://mlsanity.com/paper/2603.06507/) (2026)
- [Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling](https://mlsanity.com/paper/2502.05743/) (2025)
- [Adapting Self-Supervised Representations as a Latent Space for Efficient Generation](https://mlsanity.com/paper/2510.14630/) (2025)
- [Symmetrical Flow Matching: Unified Image Generation, Segmentation, and Classification with Score-Based Generative Models](https://mlsanity.com/paper/2506.10634/) (2025)
- [Representation Learning with Diffusion Models](https://mlsanity.com/paper/2210.11058/) (2022)
- [On Flow Matching KL Divergence](https://mlsanity.com/paper/2511.05480/) (2025)
- [Zero-Flow Encoders](https://mlsanity.com/paper/2602.00797/) (2026)
- [High-Performance Self-Supervised Learning by Joint Training of Flow Matching](https://mlsanity.com/paper/2512.19729/) (2025)

## Abstract (arXiv)

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.