# Invertible Diffusion Models for Compressed Sensing

arXiv: https://arxiv.org/abs/2403.17006 · HTML: https://mlsanity.com/paper/2403.17006/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 88 of its 143 references that are in the map.
- First posted on arXiv 25 Mar 2024.

## Placed in

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

## Builds on (most cited first, 30 of 88)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [SeeSR: Towards Semantics-Aware Real-World Image Super-Resolution](https://mlsanity.com/paper/2311.16518/) (2023)

## Built on by (most cited first, 12 of 12)

- [Adversarial Diffusion Compression for Real-World Image Super-Resolution](https://mlsanity.com/paper/2411.13383/) (2024)
- [Practical Compact Deep Compressed Sensing](https://mlsanity.com/paper/2411.13081/) (2024)
- [Polarization Uncertainty-Guided Diffusion Model for Color Polarization Image Demosaicking](https://mlsanity.com/paper/2602.23847/) (2026)
- [HuiYanEarth-SAR: A Foundation Model for High-Fidelity and Low-Cost Global Remote Sensing Imagery Generation](https://mlsanity.com/paper/2604.11444/) (2026)
- [Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing](https://mlsanity.com/paper/2503.08429/) (2025)
- [Sampling Innovation-Based Adaptive Compressive Sensing](https://mlsanity.com/paper/2503.13241/) (2025)
- [PolarVSR: A Unified Framework and Benchmark for Continuous Space-Time Polarization Video Reconstruction](https://mlsanity.com/paper/2605.10275/) (2026)
- [Conditional Denoising Diffusion Model-Based Robust MR Image Reconstruction from Highly Undersampled Data](https://mlsanity.com/paper/2510.06335/) (2025)
- [Reversible Efficient Diffusion for Image Fusion](https://mlsanity.com/paper/2601.20260/) (2026)
- [MTS-CSNet: Multiscale Tensor Factorization for Deep Compressive Sensing on RGB Images](https://mlsanity.com/paper/2602.07056/) (2026)
- [Degradation-Robust Fusion: An Efficient Degradation-Aware Diffusion Framework for Multimodal Image Fusion in Arbitrary Degradation Scenarios](https://mlsanity.com/paper/2604.08922/) (2026)
- [Three-Step Conditional Diffusion 3D Reconstruction for Light-Field Microscopy](https://mlsanity.com/paper/2605.24959/) (2026)

## Abstract (arXiv)

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment. Although recent methods utilize pre-trained diffusion models for image reconstruction, they struggle with slow inference and restricted adaptability to CS. To tackle these challenges, this paper proposes Invertible Diffusion Models (IDM), a novel efficient, end-to-end diffusion-based CS method. IDM repurposes a large-scale diffusion sampling process as a reconstruction model, and fine-tunes it end-to-end to recover original images directly from CS measurements, moving beyond the traditional paradigm of one-step noise estimation learning. To enable such memory-intensive end-to-end fine-tuning, we propose a novel two-level invertible design to transform both (1) multi-step sampling process and (2) noise estimation U-Net in each step into invertible networks. As a result, most intermediate features are cleared during training to reduce up to 93.8% GPU memory. In addition, we develop a set of lightweight modules to inject measurements into noise estimator to further facilitate reconstruction. Experiments demonstrate that IDM outperforms existing state-of-the-art CS networks by up to 2.64dB in PSNR. Compared to the recent diffusion-based approach DDNM, our IDM achieves up to 10.09dB PSNR gain and 14.54 times faster inference. Code is available at https://github.com/Guaishou74851/IDM.