Diverging Flows: Detecting Extrapolations in Conditional Generation

TL;DR

Diverging Flows tackles the safety-risks of extrapolation in conditional flow models by embedding a geometric mechanism that makes off-manifold inputs diverge rather than follow efficient transport paths. The method jointly learns predictive densities and an extrapolation indicator through contrastive vector-field regularization, adversarial negative mining, and a DOT-based detection score calibrated with split conformal prediction. Empirical results across synthetic manifolds, ERA5 weather data, and cross-domain style transfer demonstrate robust detection of extrapolations (high AUROC) without sacrificing predictive fidelity, latency, or generative quality. The work offers a practical, single-model solution for trustworthy flow-based regression and generation in high-stakes domains such as climate science, robotics, and medicine.

Abstract

The ability of Flow Matching (FM) to model complex conditional distributions has established it as the state-of-the-art for prediction tasks (e.g., robotics, weather forecasting). 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, cross-domain style transfer, and weather temperature forecasting, 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 trustworthy flow models, paving the way for reliable deployment in domains such as medicine, robotics, and climate science.

Figures (8)

• Figure 1: Conceptual overview of Diverging Flows. (Top) Flow Matching minimizes transport cost everywhere, forcing off-manifold inputs (red) to converge silently. (Bottom) Diverging Flows breaks this symmetry by enforcing transport inefficiency for invalid conditions. This ensures valid conditions ($c$) induce optimal flows, while off-manifold inputs ($\tilde{c}$) trigger detectable divergence.
• Figure 2: Vector Dynamics on Synthetic Manifolds. Two experiments, Probabilistic Regression (left), with horizon of 10 steps, and Conditional Generation (right). Top: Standard FM forces smooth convergence for all inputs, causing silent hallucinations. Bottom: Diverging Flows learns a conservative field: on-manifold inputs (green) follow optimal paths, while off-manifold queries (orange) trigger divergent flows, creating a geometric detection signal.
• Figure 3: High-Fidelity Forecasts with Diverging Flows. (Top) Visual comparison of 6-hour temperature forecasts. Diverging Flows accurately captures complex thermal fronts and fine-grained dynamics with MSE and SSIM of 0.0004 and 0.961 respectively, demonstrating that the regularization for hallucination detection does not compromise the model's capacity for precise physical regression. (Bottom) Comparison of the behavior of Diverging Flows and FM when an invalid condition is encountered.
• Figure 4: Generative Quality in Cross-Domain Transfer. Samples mapping structural inputs (MNIST) to street-view imagery (SVHN). Diverging Flows preserves the semantic identity of the digit. This demonstrates that regularization targets invalid semantics without restricting diversity.
• Figure 5: Detection Landscape: Conditional Generation. The standard model (a) fails to distinguish the manifold from the background. Diverging Flows (b) successfully identifies the ambient space as invalid (red), accepting only the spiral support.