# TabResFlow: A Normalizing Spline Flow Model for Probabilistic Univariate Tabular Regression

arXiv: https://arxiv.org/abs/2508.17056 · HTML: https://mlsanity.com/paper/2508.17056/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 23 Aug 2025.

## Builds on (most cited first, 25 of 25)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training](https://mlsanity.com/paper/2106.01342/) (2021)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Neural Oblivious Decision Ensembles for Deep Learning on Tabular Data](https://mlsanity.com/paper/1909.06312/) (2019)
- [On Embeddings for Numerical Features in Tabular Deep Learning](https://mlsanity.com/paper/2203.05556/) (2022)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Uncertainty in Gradient Boosting via Ensembles](https://mlsanity.com/paper/2006.10562/) (2020)
- [Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans and Bayesian Inference](https://mlsanity.com/paper/1807.00499/) (2018)
- [Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression](https://mlsanity.com/paper/2106.01682/) (2021)
- [XGBoostLSS -- An extension of XGBoost to probabilistic forecasting](https://mlsanity.com/paper/1907.03178/) (2019)
- [Quantifying and Explaining Machine Learning Uncertainty in Predictive Process Monitoring: An Operations Research Perspective](https://mlsanity.com/paper/2304.06412/) (2023)
- [TreeFlow: Going beyond Tree-based Gaussian Probabilistic Regression](https://mlsanity.com/paper/2206.04140/) (2022)
- [ProbSAINT: Probabilistic Tabular Regression for Used Car Pricing](https://mlsanity.com/paper/2403.03812/) (2024)

## Built on by (most cited first, 2 of 2)

- [Optimal Mixture-of-Experts Model Averaging for Conditional Generative Models](https://mlsanity.com/paper/2607.04360/) (2026)
- [Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2608.11114/) (2026)

## Abstract (arXiv)

Tabular regression is a well-studied problem with numerous industrial applications, yet most existing approaches focus on point estimation, often leading to overconfident predictions. This issue is particularly critical in industrial automation, where trustworthy decision-making is essential. Probabilistic regression models address this challenge by modeling prediction uncertainty. However, many conventional methods assume a fixed-shape distribution (typically Gaussian), and resort to estimating distribution parameters. This assumption is often restrictive, as real-world target distributions can be highly complex. To overcome this limitation, we introduce TabResFlow, a Normalizing Spline Flow model designed specifically for univariate tabular regression, where commonly used simple flow networks like RealNVP and Masked Autoregressive Flow (MAF) are unsuitable. TabResFlow consists of three key components: (1) An MLP encoder for each numerical feature. (2) A fully connected ResNet backbone for expressive feature extraction. (3) A conditional spline-based normalizing flow for flexible and tractable density estimation. We evaluate TabResFlow on nine public benchmark datasets, demonstrating that it consistently surpasses existing probabilistic regression models on likelihood scores. Our results demonstrate 9.64% improvement compared to the strongest probabilistic regression model (TreeFlow), and on average 5.6 times speed-up in inference time compared to the strongest deep learning alternative (NodeFlow). Additionally, we validate the practical applicability of TabResFlow in a real-world used car price prediction task under selective regression. To measure performance in this setting, we introduce a novel Area Under Risk Coverage (AURC) metric and show that TabResFlow achieves superior results across this metric.