# Flow-Induced Diagonal Gaussian Processes

arXiv: https://arxiv.org/abs/2509.17153 · HTML: https://mlsanity.com/paper/2509.17153/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 62 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (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)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [High-Resolution Representations for Labeling Pixels and Regions](https://mlsanity.com/paper/1904.04514/) (2019)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradient](https://mlsanity.com/paper/1811.04504/) (2018)
- [Preconditioning Kernel Matrices](https://mlsanity.com/paper/1602.06693/) (2016)
- [A Tutorial on Sparse Gaussian Processes and Variational Inference](https://mlsanity.com/paper/2012.13962/) (2020)
- [Encoding the latent posterior of Bayesian Neural Networks for uncertainty quantification](https://mlsanity.com/paper/2012.02818/) (2020)
- [Sparse Uncertainty Representation in Deep Learning with Inducing Weights](https://mlsanity.com/paper/2105.14594/) (2021)
- [Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurements](https://mlsanity.com/paper/2103.01259/) (2021)
- [Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes](https://mlsanity.com/paper/2412.20375/) (2024)

## Built on by (most cited first, 1 of 1)

- [Bayesian-LoRA: Probabilistic Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2601.21003/) (2026)

## Abstract (arXiv)

We present Flow-Induced Diagonal Gaussian Processes (FiD-GP), a compression framework that incorporates a compact inducing weight matrix to project a neural network's weight uncertainty into a lower-dimensional subspace. Critically, FiD-GP relies on normalising-flow priors and spectral regularisations to augment its expressiveness and align the inducing subspace with feature-gradient geometry through a numerically stable projection mechanism objective. Furthermore, we demonstrate how the prediction framework in FiD-GP can help to design a single-pass projection for Out-of-Distribution (OoD) detection. Our analysis shows that FiD-GP improves uncertainty estimation ability on various tasks compared with SVGP-based baselines, satisfies tight spectral residual bounds with theoretically guaranteed OoD detection, and significantly compresses the neural network's storage requirements at the cost of increased inference computation dependent on the number of inducing weights employed. Specifically, in a comprehensive empirical study spanning regression, image classification, semantic segmentation, and out-of-distribution detection benchmarks, it cuts Bayesian training cost by several orders of magnitude, compresses parameters by roughly 51%, reduces model size by about 75%, and matches state-of-the-art accuracy and uncertainty estimation.