# Towards Intrinsically Calibrated Uncertainty Quantification in Industrial Data-Driven Models via Diffusion Sampler

arXiv: https://arxiv.org/abs/2604.01870 · HTML: https://mlsanity.com/paper/2604.01870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 18 of its 48 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 18 of 18)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpoint](https://mlsanity.com/paper/1412.4430/) (2014)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations](https://mlsanity.com/paper/2102.06559/) (2021)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Adjoint Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2506.22565/) (2025)

## Abstract (arXiv)

In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification (UQ) is equally critical for safety, reliability, and decision-making, but remains a major challenge in current data-driven approaches. In this work, we introduce a diffusion-based posterior sampling framework that inherently produces well-calibrated predictive uncertainty via faithful posterior sampling, eliminating the need for post-hoc calibration. In extensive evaluations on synthetic distributions, the Raman-based phenylacetic acid soft sensor benchmark, and a real ammonia synthesis case study, our method achieves practical improvements over existing UQ techniques in both uncertainty calibration and predictive accuracy. These results highlight diffusion samplers as a principled and scalable paradigm for advancing uncertainty-aware modeling in industrial applications.