# Diffusion Posterior Sampler for Hyperspectral Unmixing with Spectral Variability Modeling

arXiv: https://arxiv.org/abs/2512.09871 · HTML: https://mlsanity.com/paper/2512.09871/

## 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 14 of its 58 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and Survey](https://mlsanity.com/paper/1708.05125/) (2017)
- [EndNet: Sparse AutoEncoder Network for Endmember Extraction and Hyperspectral Unmixing](https://mlsanity.com/paper/1708.01894/) (2017)
- [Deep Hyperspectral Unmixing using Transformer Network](https://mlsanity.com/paper/2203.17076/) (2022)
- [SAR Despeckling using a Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2206.04514/) (2022)
- [Semiblind Hyperspectral Unmixing in the Presence of Spectral Library Mismatches](https://mlsanity.com/paper/1507.01661/) (2015)
- [A Probabilistic Approach to Wildfire Spread Prediction Using a Denoising Diffusion Surrogate Model](https://mlsanity.com/paper/2507.00761/) (2025)
- [Spectral Unmixing: A Derivation of the Extended Linear Mixing Model from the Hapke Model](https://mlsanity.com/paper/1903.12089/) (2019)

## Abstract (arXiv)

Linear spectral mixture models (LMM) provide a concise form to disentangle the constituent materials (endmembers) and their corresponding proportions (abundance) in a single pixel. The critical challenges are how to model the spectral prior distribution and spectral variability. Prior knowledge and spectral variability can be rigorously modeled under the Bayesian framework, where posterior estimation of Abundance is derived by combining observed data with endmember prior distribution. Considering the key challenges and the advantages of the Bayesian framework, a novel method using a diffusion posterior sampler for semiblind unmixing, denoted as DPS4Un, is proposed to deal with these challenges with the following features: (1) we view the pretrained conditional spectrum diffusion model as a posterior sampler, which can combine the learned endmember prior with observation to get the refined abundance distribution. (2) Instead of using the existing spectral library as prior, which may raise bias, we establish the image-based endmember bundles within superpixels, which are used to train the endmember prior learner with diffusion model. Superpixels make sure the sub-scene is more homogeneous. (3) Instead of using the image-level data consistency constraint, the superpixel-based data fidelity term is proposed. (4) The endmember is initialized as Gaussian noise for each superpixel region, DPS4Un iteratively updates the abundance and endmember, contributing to spectral variability modeling. The experimental results on three real-world benchmark datasets demonstrate that DPS4Un outperforms the state-of-the-art hyperspectral unmixing methods.