Provably Safe Generative Sampling with Constricting Barrier Functions

TL;DR

This paper introduces a formal safety filtering method for flow-based generative models, ensuring generated samples meet hard constraints with minimal deviation, applicable across various domains without retraining.

Contribution

It proposes a novel safety filtering framework using Control Barrier Functions to guarantee constraint satisfaction during sampling without retraining the generative model.

Findings

Achieves 100% constraint satisfaction in experiments.

Minimizes distributional shift measured by KL divergence.

Applicable to image generation, trajectory sampling, and robotic manipulation.

Abstract

Flow-based generative models, such as diffusion models and flow matching models, have achieved remarkable success in learning complex data distributions. However, a critical gap remains for their deployment in safety-critical domains: the lack of formal guarantees that generated samples will satisfy hard constraints. We address this by proposing a safety filtering framework that acts as an online shield for any pre-trained generative model. Our key insight is to cooperate with the generative process rather than override it. We define a constricting safety tube that is relaxed at the initial noise distribution and progressively tightens to the target safe set at the final data distribution, mirroring the coarse-to-fine structure of the generative process itself. By characterizing this tube via Control Barrier Functions (CBFs), we synthesize a feedback control input through a convex Quadratic Program (QP) at each sampling step. As the tube is loosest when noise is high and intervention is cheapest in terms of control energy, most constraint enforcement occurs when it least disrupts the model's learned structure. We prove that this mechanism guarantees safe sampling while minimizing the distributional shift from the original model at each sampling step, as quantified by the KL divergence. Our framework applies to any pre-trained flow-based generative scheme requiring no retraining or architectural modifications. We validate the approach across constrained image generation, physically-consistent trajectory sampling, and safe robotic manipulation policies, achieving 100% constraint satisfaction while preserving semantic fidelity.