HybridFlow is a modular hybrid architecture that integrates aleatoric and epistemic uncertainty. It estimates aleatoric uncertainty using a conditional masked autoregressive regularization flow, and models epistemic uncertainty through flexible probabilistic predictors. HybridFlow outperforms existing uncertainty quantification frameworks on a variety of regression tasks, including depth estimation, regression benchmarks, and ice sheet emulation scientific research. Furthermore, we demonstrate that the uncertainty quantified by HybridFlow is compensated and matches model error better than existing methods for quantifying aleatoric and epistemic uncertainty.