# Diffusion model for gradient preconditioning in hyperspectral imaging inverse problems

arXiv: https://arxiv.org/abs/2507.23065 · HTML: https://mlsanity.com/paper/2507.23065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 5 of 5)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Residual Denoising Diffusion Models](https://mlsanity.com/paper/2308.13712/) (2023)
- [Estimation of the sample covariance matrix from compressive measurements](https://mlsanity.com/paper/1512.08887/) (2015)
- [Covariance Estimation from Compressive Data Partitions using a Projected Gradient-based Algorithm](https://mlsanity.com/paper/2101.04027/) (2021)
- [Latent Diffusion U-Net Representations Contain Positional Embeddings and Anomalies](https://mlsanity.com/paper/2504.07008/) (2025)

## Abstract (arXiv)

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints. A common workaround is to partition measurements and estimate local statistics-such as the covariance matrix-using only partial observations. However, this strategy introduces noise in the optimization gradients, especially when each partition contains few samples. In this work, we reinterpret this accumulation of gradient noise as a diffusion process, where successive partitions inject increasing uncertainty into the learning signal. Building on this insight, we propose a novel framework that leverages denoising diffusion models to learn a reverse process in gradient space. The model is trained to map noisy gradient estimates toward clean, well-conditioned updates, effectively preconditioning the optimization. Our approach bridges generative modeling and inverse problem solving, improving convergence and reconstruction quality under aggressive sampling regimes. We validate our method on hyperspectral recovery tasks, demonstrating significant gains in accuracy and stability over traditional optimization pipelines.