Score-Based Diffusion Priors for Adaptive Conformal Inference under Distribution Shift

Xiangyu Jiang
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:2517-2537, 2026.

Abstract

Conformal prediction provides a distribution-free coverage guarantee for predictive inference, yet its validity degrades under distribution shift, a common challenge in real-world deployment. We introduce {DiffConf}, a framework that uses score-based diffusion models as expressive priors over the data-generating process to enable adaptive conformal inference under temporal and covariate distribution shifts. The main idea is that the score function learned by a diffusion model encodes rich geometric information about the data manifold, which can be repurposed to construct nonconformity scores that are sensitive to distributional changes. We derive a diffusion-guided conformity score that integrates the learned score field with a lightweight online recalibration mechanism, providing finite-sample marginal coverage guarantees even when the data distribution evolves over time. Theoretically, we establish that {DiffConf} achieves asymptotic conditional coverage under mild regularity conditions on the drift rate, and we prove a regret bound that scales gracefully with the complexity of the distribution shift. Experiments on synthetic benchmarks, real-world tabular regression tasks, and high-dimensional image datasets demonstrate that {DiffConf} produces prediction sets that are simultaneously valid and more efficient than existing adaptive conformal methods, reducing average set size by 6–39% across the real-data benchmarks (and by over 50% under large synthetic mean shifts) while keeping coverage within one point of target.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-jiang26a, title = {Score-Based Diffusion Priors for Adaptive Conformal Inference under Distribution Shift}, author = {Jiang, Xiangyu}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {2517--2537}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/jiang26a/jiang26a.pdf}, url = {https://proceedings.mlr.press/v337/jiang26a.html}, abstract = {Conformal prediction provides a distribution-free coverage guarantee for predictive inference, yet its validity degrades under distribution shift, a common challenge in real-world deployment. We introduce {DiffConf}, a framework that uses score-based diffusion models as expressive priors over the data-generating process to enable adaptive conformal inference under temporal and covariate distribution shifts. The main idea is that the score function learned by a diffusion model encodes rich geometric information about the data manifold, which can be repurposed to construct nonconformity scores that are sensitive to distributional changes. We derive a diffusion-guided conformity score that integrates the learned score field with a lightweight online recalibration mechanism, providing finite-sample marginal coverage guarantees even when the data distribution evolves over time. Theoretically, we establish that {DiffConf} achieves asymptotic conditional coverage under mild regularity conditions on the drift rate, and we prove a regret bound that scales gracefully with the complexity of the distribution shift. Experiments on synthetic benchmarks, real-world tabular regression tasks, and high-dimensional image datasets demonstrate that {DiffConf} produces prediction sets that are simultaneously valid and more efficient than existing adaptive conformal methods, reducing average set size by 6–39% across the real-data benchmarks (and by over 50% under large synthetic mean shifts) while keeping coverage within one point of target.} }
Endnote
%0 Conference Paper %T Score-Based Diffusion Priors for Adaptive Conformal Inference under Distribution Shift %A Xiangyu Jiang %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-jiang26a %I PMLR %P 2517--2537 %U https://proceedings.mlr.press/v337/jiang26a.html %V 337 %X Conformal prediction provides a distribution-free coverage guarantee for predictive inference, yet its validity degrades under distribution shift, a common challenge in real-world deployment. We introduce {DiffConf}, a framework that uses score-based diffusion models as expressive priors over the data-generating process to enable adaptive conformal inference under temporal and covariate distribution shifts. The main idea is that the score function learned by a diffusion model encodes rich geometric information about the data manifold, which can be repurposed to construct nonconformity scores that are sensitive to distributional changes. We derive a diffusion-guided conformity score that integrates the learned score field with a lightweight online recalibration mechanism, providing finite-sample marginal coverage guarantees even when the data distribution evolves over time. Theoretically, we establish that {DiffConf} achieves asymptotic conditional coverage under mild regularity conditions on the drift rate, and we prove a regret bound that scales gracefully with the complexity of the distribution shift. Experiments on synthetic benchmarks, real-world tabular regression tasks, and high-dimensional image datasets demonstrate that {DiffConf} produces prediction sets that are simultaneously valid and more efficient than existing adaptive conformal methods, reducing average set size by 6–39% across the real-data benchmarks (and by over 50% under large synthetic mean shifts) while keeping coverage within one point of target.
APA
Jiang, X.. (2026). Score-Based Diffusion Priors for Adaptive Conformal Inference under Distribution Shift. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:2517-2537 Available from https://proceedings.mlr.press/v337/jiang26a.html.

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