# Latent Diffusion for Missing Data

arXiv: https://arxiv.org/abs/2605.28427 · HTML: https://mlsanity.com/paper/2605.28427/

## 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 16 of its 26 references that are in the map.
- First posted on arXiv 27 May 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, 16 of 16)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Diffusion models for missing value imputation in tabular data](https://mlsanity.com/paper/2210.17128/) (2022)
- [MissDiff: Training Diffusion Models on Tabular Data with Missing Values](https://mlsanity.com/paper/2307.00467/) (2023)
- [MCFlow: Monte Carlo Flow Models for Data Imputation](https://mlsanity.com/paper/2003.12628/) (2020)
- [Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2202.04599/) (2022)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [MIWAE: Deep Generative Modelling and Imputation of Incomplete Data](https://mlsanity.com/paper/1812.02633/) (2018)
- [Score Matching With Missing Data](https://mlsanity.com/paper/2506.00557/) (2025)

## Abstract (arXiv)

Diffusion models have emerged as powerful generative approaches for missing-data imputation, yet most existing methods operate directly in data space and degrade when training data are heavily incomplete. We investigate whether shifting diffusion to a learned latent representation improves robustness under missing-completely-at-random (MCAR) corruption. To this end, we propose a two-stage framework: a robust VAE-based imputer first learns compact semantic features from incomplete observations, and a diffusion model is then trained in the resulting latent space. Across training missing rates, we perform a controlled comparison against pixel-space diffusion models under the same incomplete-data setting. The latent diffusion model maintains high sample quality and remains stable up to 50% missingness, while pixel-space diffusion degrades progressively as missingness increases. For downstream imputation, latent diffusion also achieves consistently better performance than pixel-space diffusion. These findings indicate that latent-space modeling mitigates artifact amplification from zero-imputed inputs and provides a more robust generative prior for incomplete-data learning. Overall, our results support latent diffusion as a strong and practically useful alternative to pixel-space diffusion for missing-data problems.