Conditional Flow Models Convert Epistemic Uncertainty into Apparent Aleatoric Variance

Abstract

Conditional Flow Models (CFMs) are increasingly being used in place of deterministic predictors across machine learning, including for tasks that were classically formulated as regression. Given their success in such tasks, we ask the question: what useful information do the conditional distributions produced by CFMs carry beyond what a point predictor would provide? We identify a systematic phenomenon: in many natural regimes, CFM samples routinely have larger variance than the true conditional distribution, even in nearly deterministic regression problems. This effect is most pronounced where the model has not resolved the dependence on the conditioning variable, and thus the additional variance can be viewed as converting epistemic uncertainty in fitting the ground truth conditional distribution into apparent aleatoric variance in the generated samples. Through controlled synthetic and real-data experiments, and comparisons with explicit smoothing estimators, we show that the induced variance tracks model underfitting of complex or hard-to-fit targets, and decreases with additional training or data. We provide a theoretical account of the phenomenon in a simplified setting and demonstrate a consequent practical use-case of conditional flow-matching: designing high-coverage predictive sets that cover the ground-truth regression target.