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This paper introduces a diffusion-based posterior sampling framework for intrinsically calibrated uncertainty quantification (UQ) in data-driven industrial models. The method leverages diffusion models to directly sample from the posterior distribution, leading to well-calibrated predictive uncertainties without requiring post-hoc calibration techniques. Evaluations on synthetic data, a Raman spectroscopy benchmark, and an ammonia synthesis case study demonstrate improved UQ and predictive accuracy compared to existing methods.
Diffusion models can provide intrinsically calibrated uncertainty estimates for industrial data-driven models, finally offering a practical alternative to unreliable post-hoc calibration methods.
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.