# Missing Data Imputation under Manifold Hypothesis

arXiv: https://arxiv.org/abs/2607.03641 · HTML: https://mlsanity.com/paper/2607.03641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [CA-PCA: Manifold Dimension Estimation, Adapted for Curvature](https://mlsanity.com/paper/2309.13478/) (2023)
- [missForestPredict -- Missing data imputation for prediction settings](https://mlsanity.com/paper/2407.03379/) (2024)

## Abstract (arXiv)

The manifold hypothesis posits that high-dimensional data are concentrated near a low-dimensional embedded manifold. Recent advances in mixture variational autoencoders (VAEs) provide a powerful tool for extracting such underlying structure in a faithful manner. The resulting geometric structure naturally introduces local and global relationships among variables, thereby providing a systematic way of imputing missing data. We propose a model-based imputation method that enables sampling from ( p(bmxmis mid bmxobs) ) via a sampling-importance-resampling (SIR) procedure, which can be further augmented with a joint diffusion model in the latent space. Our method imputes missing data while respecting the underlying geometry, achieves competitive performance compared to state-of-the-art procedures, quantifies uncertainty in the imputations, and is model-based, thereby enabling on-the-fly imputation without rerunning the entire procedure.