[Paper] Diffusion Posterior Sampler for Hyperspectral Unmixing with Spectral Variability Modeling

Source: arXiv - 2512.09871v1

Overview

This paper introduces DPS4Un, a diffusion‑based posterior sampler that tackles hyperspectral unmixing while explicitly handling spectral variability. By treating a pretrained conditional diffusion model as a Bayesian posterior engine, the authors blend learned endmember priors with observed pixel data, achieving more accurate abundance estimates than existing methods.

Key Contributions

• Diffusion Posterior Sampler for Unmixing – Recasts a conditional spectrum diffusion model as a Bayesian posterior sampler, enabling joint refinement of endmember spectra and abundances.
• Image‑Based Endmember Bundles – Constructs endmember priors from superpixel‑derived bundles instead of relying on external spectral libraries, reducing bias and better capturing scene‑specific variability.
• Superpixel‑Level Data Fidelity – Introduces a data consistency term that operates at the superpixel level, preserving local homogeneity while allowing variability across regions.
• Iterative Endmember‑Abundance Update – Starts each superpixel’s endmember estimate from Gaussian noise and alternates between abundance inference and endmember refinement, naturally modeling spectral variability.
• State‑of‑the‑Art Performance – Demonstrates superior results on three benchmark hyperspectral datasets compared to leading unmixing algorithms.

Methodology

1. Superpixel Segmentation – The hyperspectral image is partitioned into superpixels, each assumed to contain a relatively homogeneous mixture of materials.
2. Endmember Bundle Creation – Within each superpixel, the raw spectra are clustered to form a small “bundle” that captures local variability. These bundles serve as training data for the diffusion prior.
3. Conditional Diffusion Model – A diffusion network is pretrained to model the distribution of endmember spectra conditioned on the observed pixel values. In diffusion terms, the model learns to denoise a noisy spectrum back to a plausible endmember sample.
4. Posterior Sampling (DPS4Un) – During inference, the diffusion model acts as a sampler: starting from Gaussian noise, it iteratively refines endmember candidates while simultaneously updating abundance maps to satisfy the superpixel‑level data fidelity term.
5. Alternating Optimization – The algorithm alternates between (a) sampling endmembers from the diffusion posterior and (b) solving a constrained least‑squares problem for abundances, repeating until convergence.

Results & Findings

• Quantitative Gains: Across the three real‑world datasets (e.g., Urban, Jasper Ridge, and Cuprite), DPS4Un reduced the root‑mean‑square error (RMSE) of abundance estimates by 10–15 % relative to the previous best Bayesian unmixing methods.
• Spectral Variability Capture: Visual inspection of reconstructed spectra showed tighter alignment with ground‑truth endmembers, especially in regions with strong illumination changes or material aging.
• Robustness to Library Bias: By using image‑derived bundles, DPS4Un avoided the systematic bias observed when external spectral libraries were employed, leading to more consistent performance across diverse scenes.
• Computational Trade‑off: The diffusion sampling adds roughly 2× runtime compared to classic linear unmixing, but remains tractable on modern GPUs (≈ 0.8 s per 100 × 100 pixel patch).

Practical Implications

• Better Material Quantification: Remote‑sensing analysts can obtain more reliable abundance maps for applications like mineral exploration, precision agriculture, and environmental monitoring.
• Plug‑and‑Play Prior Learning: The diffusion prior can be retrained on any new scene, allowing developers to adapt the model to domain‑specific sensors without curating large external libraries.
• Integration with Existing Pipelines: DPS4Un’s alternating update scheme can be wrapped around standard linear unmixing codebases, offering a drop‑in upgrade for projects that already segment images into superpixels.
• Edge‑Device Feasibility: Since the diffusion model inference is the dominant cost, lightweight distilled versions could run on edge GPUs for near‑real‑time unmixing on UAV‑borne hyperspectral cameras.

Limitations & Future Work

• Computational Overhead – The iterative diffusion sampling is more expensive than closed‑form LMM solutions; optimizing the number of diffusion steps or employing faster samplers is an open avenue.
• Superpixel Dependency – The quality of the endmember bundles hinges on the superpixel segmentation; poorly chosen superpixels can degrade performance. Adaptive or learned segmentation could improve robustness.
• Scalability to Very Large Scenes – While patch‑wise processing works, end‑to‑end training on gigapixel hyperspectral mosaics remains challenging.
• Extension to Non‑Linear Mixing – The current framework assumes a linear mixture model; future research may explore diffusion‑based posterior sampling for more complex non‑linear mixing physics.

Authors

• Yimin Zhu
• Lincoln Linlin Xu

Paper Information

• arXiv ID: 2512.09871v1
• Categories: cs.CV
• Published: December 10, 2025
• PDF: Download PDF