# iUNets: Fully invertible U-Nets with Learnable Up- and Downsampling

arXiv: https://arxiv.org/abs/2005.05220 · HTML: https://mlsanity.com/paper/2005.05220/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2020.

## Built on by (most cited first, 7 of 7)

- [Reversible Vision Transformers](https://mlsanity.com/paper/2302.04869/) (2023)
- [Efficient Regression-Based Training of Normalizing Flows for Boltzmann Generators](https://mlsanity.com/paper/2506.01158/) (2025)
- [Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces](https://mlsanity.com/paper/2205.14627/) (2022)
- [A Unified Framework for Forward and Inverse Problems in Subsurface Imaging using Latent Space Translations](https://mlsanity.com/paper/2410.11247/) (2024)
- [Beyond NaN: Resiliency of Optimization Layers in The Face of Infeasibility](https://mlsanity.com/paper/2202.06242/) (2022)
- [FetusMapV2: Enhanced Fetal Pose Estimation in 3D Ultrasound](https://mlsanity.com/paper/2310.19293/) (2023)
- [Bringing together invertible UNets with invertible attention modules for memory-efficient diffusion models](https://mlsanity.com/paper/2504.10883/) (2025)

## Abstract (arXiv)

U-Nets have been established as a standard architecture for image-to-image learning problems such as segmentation and inverse problems in imaging. For large-scale data, as it for example appears in 3D medical imaging, the U-Net however has prohibitive memory requirements. Here, we present a new fully-invertible U-Net-based architecture called the iUNet, which employs novel learnable and invertible up- and downsampling operations, thereby making the use of memory-efficient backpropagation possible. This allows us to train deeper and larger networks in practice, under the same GPU memory restrictions. Due to its invertibility, the iUNet can furthermore be used for constructing normalizing flows.