CONFLO: Conformal Prediction with Conditional Coverage via Normalizing Flow

ICLR 2026 Conference Submission20865 Authors

Keywords: Quantile, Regularization, Classification

Abstract: Beyond point predictions, conformal prediction provides prediction sets that enjoy finite-sample probability coverage guarantees, but only at the population level. In practice, prediction sets can under- or over-cover in subpopulations, limiting their usability for individual predictions. To address this issue, we propose \CONFLO, a conformal prediction framework that integrates conditional normalizing flows (CNF) with a novel form of regularization. The anchoring idea is to transform raw nonconformity scores through a feature-dependent bijection into new scores that are (nearly) independent of the inputs. Since independence cannot be perfectly achieved in practice, we add a quantile-aligning penalty to the loss function as an additional tactic to enforce common conditional coverage across user-specified groups. Experiments on diverse datasets demonstrate that CONFLO improves conditional coverage across subpopulations and sizes of prediction sets compared to baseline methods and competitors like APS and RAPS. Theoretical results are provided demonstrating that our algorithm achieves conditional coverage asymptotically.

Primary Area: generative models

Submission Number: 20865