# Tackling Ill-posedness of Reversible Image Conversion with Well-posed Invertible Network

arXiv: https://arxiv.org/abs/2508.02111 · HTML: https://mlsanity.com/paper/2508.02111/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 89 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Blind Super-Resolution With Iterative Kernel Correction](https://mlsanity.com/paper/1904.03377/) (2019)
- [Real-Time User-Guided Image Colorization with Learned Deep Priors](https://mlsanity.com/paper/1705.02999/) (2017)
- [EditGuard: Versatile Image Watermarking for Tamper Localization and Copyright Protection](https://mlsanity.com/paper/2312.08883/) (2023)
- [Invertible Image Signal Processing](https://mlsanity.com/paper/2103.15061/) (2021)
- [Transcending the Limit of Local Window: Advanced Super-Resolution Transformer with Adaptive Token Dictionary](https://mlsanity.com/paper/2401.08209/) (2024)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Learned Image Downscaling for Upscaling using Content Adaptive Resampler](https://mlsanity.com/paper/1907.12904/) (2019)
- [CRoSS: Diffusion Model Makes Controllable, Robust and Secure Image Steganography](https://mlsanity.com/paper/2305.16936/) (2023)
- [OmniGuard: Hybrid Manipulation Localization via Augmented Versatile Deep Image Watermarking](https://mlsanity.com/paper/2412.01615/) (2024)
- [Recursive Generalization Transformer for Image Super-Resolution](https://mlsanity.com/paper/2303.06373/) (2023)
- [Large-capacity and Flexible Video Steganography via Invertible Neural Network](https://mlsanity.com/paper/2304.12300/) (2023)
- [Towards Bidirectional Arbitrary Image Rescaling: Joint Optimization and Cycle Idempotence](https://mlsanity.com/paper/2203.00911/) (2022)

## Abstract (arXiv)

Reversible image conversion (RIC) suffers from ill-posedness issues due to its forward conversion process being considered an underdetermined system. Despite employing invertible neural networks (INN), existing RIC methods intrinsically remain ill-posed as inevitably introducing uncertainty by incorporating randomly sampled variables. To tackle the ill-posedness dilemma, we focus on developing a reliable approximate left inverse for the underdetermined system by constructing an overdetermined system with a non-zero Gram determinant, thus ensuring a well-posed solution. Based on this principle, we propose a well-posed invertible 1×1 convolution (WIC), which eliminates the reliance on random variable sampling and enables the development of well-posed invertible networks. Furthermore, we design two innovative networks, WIN-Na"ive and WIN, with the latter incorporating advanced skip-connections to enhance long-term memory. Our methods are evaluated across diverse RIC tasks, including reversible image hiding, image rescaling, and image decolorization, consistently achieving state-of-the-art performance. Extensive experiments validate the effectiveness of our approach, demonstrating its ability to overcome the bottlenecks of existing RIC solutions and setting a new benchmark in the field. Codes are available in https://github.com/BNU-ERC-ITEA/WIN.