Native Extrapolation Awareness in Flow-Based Conditional Generation

The ability of Flow Matching (FM) to model complex conditional distributions has established it as a state-of-the-art approach for scientific machine learning (e.g., weather forecasting, drug design). However, deployment in safety-critical settings is hindered by a critical extrapolation hazard: driven by smoothness biases, flow models yield plausible outputs even for off-manifold conditions, resulting in silent failures indistinguishable from valid predictions. In this work, we introduce Diverging Flows, a novel approach that enables a single model to simultaneously perform conditional generation and native extrapolation detection by structurally enforcing inefficient transport for off-manifold inputs. We evaluate our method on synthetic manifolds, weather forecasting, and cross-domain style transfer, demonstrating that it achieves effective detection of extrapolations without compromising predictive fidelity or inference latency. These results establish Diverging Flows as a robust solution for safety-critical regression (e.g., robotics) and trustworthy predictions in scientific fields such as climate science and molecular design.