# Volumetric Material Decomposition Using Spectral Diffusion Posterior Sampling with a Compressed Polychromatic Forward Model

arXiv: https://arxiv.org/abs/2503.22392 · HTML: https://mlsanity.com/paper/2503.22392/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 6 of its 18 references that are in the map.
- First posted on arXiv 28 Mar 2025.

## Placed in

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

## Builds on (most cited first, 6 of 6)

- [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 New 2.5D Representation for Lymph Node Detection using Random Sets of Deep Convolutional Neural Network Observations](https://mlsanity.com/paper/1406.2639/) (2014)
- [Automated 3D Segmentation of Kidneys and Tumors in MICCAI KiTS 2023 Challenge](https://mlsanity.com/paper/2310.04110/) (2023)
- [Strategies for CT Reconstruction using Diffusion Posterior Sampling with a Nonlinear Model](https://mlsanity.com/paper/2407.12956/) (2024)
- [CTorch: PyTorch-Compatible GPU-Accelerated Auto-Differentiable Projector Toolbox for Computed Tomography](https://mlsanity.com/paper/2503.16741/) (2025)

## Built on by (most cited first, 2 of 2)

- [SpectralCTGaussians: Projection-Domain Reconstruction and Basis Material Decomposition for Spectral CT using 3D Gaussian Splatting](https://mlsanity.com/paper/2609.29638/) (2026)
- [Gaussian Material Fields for Volumetric Multi-Energy CT Decomposition](https://mlsanity.com/paper/2610.09492/) (2026)

## Abstract (arXiv)

We have previously introduced Spectral Diffusion Posterior Sampling (Spectral DPS) as a framework for accurate one-step material decomposition by integrating analytic spectral system models with priors learned from large datasets. This work extends the 2D Spectral DPS algorithm to 3D by addressing potentially limiting large-memory requirements with a pre-trained 2D diffusion model for slice-by-slice processing and a compressed polychromatic forward model to ensure accurate physical modeling. Simulation studies demonstrate that the proposed memory-efficient 3D Spectral DPS enables material decomposition of clinically significant volume sizes. Quantitative analysis reveals that Spectral DPS outperforms other deep-learning algorithms, such as InceptNet and conditional DDPM in contrast quantification, inter-slice continuity, and resolution preservation. This study establishes a foundation for advancing one-step material decomposition in volumetric spectral CT.