# Proximal Residual Flows for Bayesian Inverse Problems

arXiv: https://arxiv.org/abs/2211.17158 · HTML: https://mlsanity.com/paper/2211.17158/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 46 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 30 of 35)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [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)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport](https://mlsanity.com/paper/2006.00104/) (2020)
- [The Singular Values of Convolutional Layers](https://mlsanity.com/paper/1805.10408/) (2018)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [Block Neural Autoregressive Flow](https://mlsanity.com/paper/1904.04676/) (2019)
- [Learning Maximally Monotone Operators for Image Recovery](https://mlsanity.com/paper/2012.13247/) (2020)
- [Can Push-forward Generative Models Fit Multimodal Distributions?](https://mlsanity.com/paper/2206.14476/) (2022)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [Convolutional Proximal Neural Networks and Plug-and-Play Algorithms](https://mlsanity.com/paper/2011.02281/) (2020)
- [Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint](https://mlsanity.com/paper/2109.11375/) (2021)

## Built on by (most cited first, 5 of 5)

- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [Importance Corrected Neural JKO Sampling](https://mlsanity.com/paper/2407.20444/) (2024)
- [Invertible ResNets for Inverse Imaging Problems: Competitive Performance with Provable Regularization Properties](https://mlsanity.com/paper/2409.13482/) (2024)
- [Mixed Noise and Posterior Estimation with Conditional DeepGEM](https://mlsanity.com/paper/2402.02964/) (2024)
- [Task Switching Without Forgetting via Proximal Decoupling](https://mlsanity.com/paper/2604.18857/) (2026)

## Abstract (arXiv)

Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows. Based on the fact, that proximal neural networks are by definition averaged operators, we ensure invertibility of certain residual blocks. Moreover, we extend the architecture to conditional proximal residual flows for posterior reconstruction within Bayesian inverse problems. We demonstrate the performance of proximal residual flows on numerical examples.