# Benchmarking Invertible Architectures on Inverse Problems

arXiv: https://arxiv.org/abs/2101.10763 · HTML: https://mlsanity.com/paper/2101.10763/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 14 references that are in the map.
- First posted on arXiv 26 Jan 2021.

## Builds on (most cited first, 10 of 10)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [Invertible Autoencoder for domain adaptation](https://mlsanity.com/paper/1802.06869/) (2018)

## Built on by (most cited first, 25 of 25)

- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [Consistency Models for Scalable and Fast Simulation-Based Inference](https://mlsanity.com/paper/2312.05440/) (2023)
- [Autoinverse: Uncertainty Aware Inversion of Neural Networks](https://mlsanity.com/paper/2208.13780/) (2022)
- [Inverse design of two-dimensional materials with invertible neural networks](https://mlsanity.com/paper/2106.03013/) (2021)
- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows](https://mlsanity.com/paper/2110.04227/) (2021)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Inverse deep learning methods and benchmarks for artificial electromagnetic material design](https://mlsanity.com/paper/2112.10254/) (2021)
- [Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference](https://mlsanity.com/paper/2105.05489/) (2021)
- [Tackling Multimodal Device Distributions in Inverse Photonic Design using Invertible Neural Networks](https://mlsanity.com/paper/2208.14212/) (2022)
- [Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances](https://mlsanity.com/paper/2310.13433/) (2023)
- [Analytically Tractable Hidden-States Inference in Bayesian Neural Networks](https://mlsanity.com/paper/2107.03759/) (2021)
- [RID-Noise: Towards Robust Inverse Design under Noisy Environments](https://mlsanity.com/paper/2112.03912/) (2021)
- [Accelerating Inverse Learning via Intelligent Localization with Exploratory Sampling](https://mlsanity.com/paper/2212.01016/) (2022)
- [Learning truly monotone operators with applications to nonlinear inverse problems](https://mlsanity.com/paper/2404.00390/) (2024)
- [ISR: Invertible Symbolic Regression](https://mlsanity.com/paper/2405.06848/) (2024)
- [Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling](https://mlsanity.com/paper/2211.14366/) (2022)
- [Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates](https://mlsanity.com/paper/2304.13860/) (2023)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Generalized Neural Operator for Parametric and Boundary-Value Problems](https://mlsanity.com/paper/2607.21932/) (2026)
- [Fast ABC with joint generative modelling and subset simulation](https://mlsanity.com/paper/2104.08156/) (2021)
- [Deep Invertible Approximation of Topologically Rich Maps between Manifolds](https://mlsanity.com/paper/2210.00577/) (2022)
- [IDToolkit: A Toolkit for Benchmarking and Developing Inverse Design Algorithms in Nanophotonics](https://mlsanity.com/paper/2305.18978/) (2023)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation](https://mlsanity.com/paper/2608.01164/) (2026)

## Abstract (arXiv)

Recent work demonstrated that flow-based invertible neural networks are promising tools for solving ambiguous inverse problems. Following up on this, we investigate how ten invertible architectures and related models fare on two intuitive, low-dimensional benchmark problems, obtaining the best results with coupling layers and simple autoencoders. We hope that our initial efforts inspire other researchers to evaluate their invertible architectures in the same setting and put forth additional benchmarks, so our evaluation may eventually grow into an official community challenge.