# Nuclear Diffusion Models for Low-Rank Background Suppression in Videos

arXiv: https://arxiv.org/abs/2509.20886 · HTML: https://mlsanity.com/paper/2509.20886/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 9 of 9)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learning](https://mlsanity.com/paper/2409.06219/) (2024)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Sequential Posterior Sampling with Diffusion Models](https://mlsanity.com/paper/2409.05399/) (2024)
- [Deep Generative Models for Bayesian Inference on High-Rate Sensor Data: Applications in Automotive Radar and Medical Imaging](https://mlsanity.com/paper/2504.12154/) (2025)

## Abstract (arXiv)

Video sequences often contain structured noise and background artifacts that obscure dynamic content, posing challenges for accurate analysis and restoration. Robust principal component methods address this by decomposing data into low-rank and sparse components. Still, the sparsity assumption often fails to capture the rich variability present in real video data. To overcome this limitation, a hybrid framework that integrates low-rank temporal modeling with diffusion posterior sampling is proposed. The proposed method, Nuclear Diffusion, is evaluated on a real-world medical imaging problem, namely cardiac ultrasound dehazing, and demonstrates improved dehazing performance compared to traditional RPCA concerning contrast enhancement (gCNR) and signal preservation (KS statistic). These results highlight the potential of combining model-based temporal models with deep generative priors for high-fidelity video restoration.