# Deep Incomplete Multi-view Learning via Cyclic Permutation of VAEs

arXiv: https://arxiv.org/abs/2502.11037 · HTML: https://mlsanity.com/paper/2502.11037/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 16 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Evaluating Text-to-Visual Generation with Image-to-Text Generation](https://mlsanity.com/paper/2404.01291/) (2024)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Multimodal Generative Models for Scalable Weakly-Supervised Learning](https://mlsanity.com/paper/1802.05335/) (2018)
- [Variational Mixture-of-Experts Autoencoders for Multi-Modal Deep Generative Models](https://mlsanity.com/paper/1911.03393/) (2019)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [A Survey of Multi-View Representation Learning](https://mlsanity.com/paper/1610.01206/) (2016)
- [Generalized Multimodal ELBO](https://mlsanity.com/paper/2105.02470/) (2021)
- [Deep Partial Multi-View Learning](https://mlsanity.com/paper/2011.06170/) (2020)
- [Multimodal Generative Learning Utilizing Jensen-Shannon-Divergence](https://mlsanity.com/paper/2006.08242/) (2020)
- [Deep Incomplete Multi-view Clustering with Cross-view Partial Sample and Prototype Alignment](https://mlsanity.com/paper/2303.15689/) (2023)
- [Incomplete Contrastive Multi-View Clustering with High-Confidence Guiding](https://mlsanity.com/paper/2312.08697/) (2023)
- [Unity by Diversity: Improved Representation Learning in Multimodal VAEs](https://mlsanity.com/paper/2403.05300/) (2024)
- [A tutorial on multi-view autoencoders using the multi-view-AE library](https://mlsanity.com/paper/2403.07456/) (2024)

## Built on by (most cited first, 8 of 8)

- [GOOD: Training-Free Guided Diffusion Sampling for Out-of-Distribution Detection](https://mlsanity.com/paper/2510.17131/) (2025)
- [Inference-Time Dynamic Modality Selection for Incomplete Multimodal Classification](https://mlsanity.com/paper/2601.22853/) (2026)
- [MacTok: Robust Continuous Tokenization for Image Generation](https://mlsanity.com/paper/2603.29634/) (2026)
- [Reasoning on the Manifold: Bidirectional Consistency for Self-Verification in Diffusion Language Models](https://mlsanity.com/paper/2604.16565/) (2026)
- [Diverse via bounded Agreement: Geometric Regularization for Multimodal Fusion](https://mlsanity.com/paper/2601.21670/) (2026)
- [DINO-VO: Learning Where to Focus for Enhanced State Estimation](https://mlsanity.com/paper/2604.04055/) (2026)
- [Beyond Independence: Learning Correlated Views for Variational Incomplete Multi-View Clustering](https://mlsanity.com/paper/2608.15757/) (2026)
- [Do More Modalities Always Help? A Geometric Perspective on Missing-Modality Robustness](https://mlsanity.com/paper/2610.04792/) (2026)

## Abstract (arXiv)

Multi-View Representation Learning (MVRL) aims to derive a unified representation from multi-view data by leveraging shared and complementary information across views. However, when views are irregularly missing, the incomplete data can lead to representations that lack sufficiency and consistency. To address this, we propose Multi-View Permutation of Variational Auto-Encoders (MVP), which excavates invariant relationships between views in incomplete data. MVP establishes inter-view correspondences in the latent space of Variational Auto-Encoders, enabling the inference of missing views and the aggregation of more sufficient information. To derive a valid Evidence Lower Bound (ELBO) for learning, we apply permutations to randomly reorder variables for cross-view generation and then partition them by views to maintain invariant meanings under permutations. Additionally, we enhance consistency by introducing an informational prior with cyclic permutations of posteriors, which turns the regularization term into a similarity measure across distributions. We demonstrate the effectiveness of our approach on seven diverse datasets with varying missing ratios, achieving superior performance in multi-view clustering and generation tasks.