# Flow-Matching Guided Deep Unfolding for Hyperspectral Image Reconstruction

arXiv: https://arxiv.org/abs/2510.01912 · HTML: https://mlsanity.com/paper/2510.01912/

## 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 28 of its 76 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [Deep Learning for Hyperspectral Image Classification: An Overview](https://mlsanity.com/paper/1910.12861/) (2019)
- [Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2111.07910/) (2021)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [MST++: Multi-stage Spectral-wise Transformer for Efficient Spectral Reconstruction](https://mlsanity.com/paper/2204.07908/) (2022)
- [Coarse-to-Fine Sparse Transformer for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2203.04845/) (2022)
- [HDNet: High-resolution Dual-domain Learning for Spectral Compressive Imaging](https://mlsanity.com/paper/2203.02149/) (2022)
- [Degradation-Aware Unfolding Half-Shuffle Transformer for Spectral Compressive Imaging](https://mlsanity.com/paper/2205.10102/) (2022)
- [Deep Gaussian Scale Mixture Prior for Spectral Compressive Imaging](https://mlsanity.com/paper/2103.07152/) (2021)
- [GAP-net for Snapshot Compressive Imaging](https://mlsanity.com/paper/2012.08364/) (2020)
- [Spectral DiffuserCam: lensless snapshot hyperspectral imaging with a spectral filter array](https://mlsanity.com/paper/2006.08565/) (2020)
- [Binarized Spectral Compressive Imaging](https://mlsanity.com/paper/2305.10299/) (2023)
- [Residual Degradation Learning Unfolding Framework with Mixing Priors across Spectral and Spatial for Compressive Spectral Imaging](https://mlsanity.com/paper/2211.06891/) (2022)
- [Pixel Adaptive Deep Unfolding Transformer for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2308.10820/) (2023)
- [Aerial Vehicle Tracking by Adaptive Fusion of Hyperspectral Likelihood Maps](https://mlsanity.com/paper/1707.03553/) (2017)
- [Latent Diffusion Prior Enhanced Deep Unfolding for Snapshot Spectral Compressive Imaging](https://mlsanity.com/paper/2311.14280/) (2023)
- [Dynamic brain spectrum acquired by a real-time ultra-spectral imaging chip with reconfigurable metasurfaces](https://mlsanity.com/paper/2005.02689/) (2020)

## Abstract (arXiv)

Reconstructing a three-dimensional hyperspectral cube from a two-dimensional compressed measurement is a severely ill-posed inverse problem. Existing deep unfolding networks (DUNs) retain fidelity to the imaging model, but regression-trained denoisers can suppress spatial detail and smooth spectral structure under strong modulation. This paper proposes FMU, a deep unfolding framework that couples a measurement-conditioned flow-matching prior with a sensing-model-guided measurement update. A two-phase scheme first learns a compact clean-HSI latent target and then trains a conditional velocity field to generate this target from Gaussian noise. A mean-velocity regularizer additionally penalizes the first-moment error of the learned field. On the KAIST 10-scene benchmark under the optical-filter setting, FMU obtains 42.13,dB PSNR and 0.9900 SSIM, outperforming LADE-DUN by 1.16,dB in PSNR under the same training data, sensing mask, and evaluation protocol. Under the same optical-filter operator, FMU is further evaluated on held-out KAIST and ICVL scenes without fine-tuning. We also report quantitative simulated-CASSI results and qualitative reconstructions of real CASSI measurements.