# JAPAN: Joint Adaptive Prediction Areas with Normalising-Flows

arXiv: https://arxiv.org/abs/2505.23196 · HTML: https://mlsanity.com/paper/2505.23196/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [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)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions](https://mlsanity.com/paper/2006.13707/) (2020)
- [PythonRobotics: a Python code collection of robotics algorithms](https://mlsanity.com/paper/1808.10703/) (2018)
- [Conformalized Adaptive Forecasting of Heterogeneous Trajectories](https://mlsanity.com/paper/2402.09623/) (2024)

## Built on by (most cited first, 4 of 4)

- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Super-Level-Set Regression: Conditional Quantiles via Volume Minimization](https://mlsanity.com/paper/2605.06210/) (2026)
- [TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Models](https://mlsanity.com/paper/2605.07100/) (2026)
- [Conformal Prediction and Conditional Coverage for Tabular Foundation Models](https://mlsanity.com/paper/2609.34887/) (2026)

## Abstract (arXiv)

Conformal prediction provides a model-agnostic framework for uncertainty quantification with finite-sample validity guarantees, making it an attractive tool for constructing reliable prediction sets. However, existing approaches commonly rely on residual-based conformity scores, which impose geometric constraints and struggle when the underlying distribution is multimodal. In particular, they tend to produce overly conservative prediction areas centred around the mean, often failing to capture the true shape of complex predictive distributions. In this work, we introduce JAPAN (Joint Adaptive Prediction Areas with Normalising-Flows), a conformal prediction framework that uses density-based conformity scores. By leveraging flow-based models, JAPAN estimates the (predictive) density and constructs prediction areas by thresholding on the estimated density scores, enabling compact, potentially disjoint, and context-adaptive regions that retain finite-sample coverage guarantees. We theoretically motivate the efficiency of JAPAN and empirically validate it across multivariate regression and forecasting tasks, demonstrating good calibration and tighter prediction areas compared to existing baselines. We also provide several extensions adding flexibility to our proposed framework.