[Paper Review] SafeDiffuser: Safe Planning with Diffusion Probabilistic Models

Wei Xiao, Tsun-Hsuan Wang+2 more|arXiv (Cornell University)|May 31, 2023

Model Reduction and Neural Networks4 citations

TL;DR

SafeDiffuser introduces finite-time diffusion invariance using control barrier functions (CBFs) to embed safety guarantees directly into the denoising process of diffusion probabilistic models for robotic planning. By integrating CBFs into the diffusion time horizon, it ensures trajectories remain within safe sets throughout generation, demonstrating robust, guaranteed-safe performance across maze navigation, legged locomotion, and 3D manipulation tasks—outperforming vanilla diffusion models in safety and reliability.

ABSTRACT

Diffusion model-based approaches have shown promise in data-driven planning, but there are no safety guarantees, thus making it hard to be applied for safety-critical applications. To address these challenges, we propose a new method, called SafeDiffuser, to ensure diffusion probabilistic models satisfy specifications by using a class of control barrier functions. The key idea of our approach is to embed the proposed finite-time diffusion invariance into the denoising diffusion procedure, which enables trustworthy diffusion data generation. Moreover, we demonstrate that our finite-time diffusion invariance method through generative models not only maintains generalization performance but also creates robustness in safe data generation. We test our method on a series of safe planning tasks, including maze path generation, legged robot locomotion, and 3D space manipulation, with results showing the advantages of robustness and guarantees over vanilla diffusion models.

Motivation & Objective

• To address the lack of safety guarantees in diffusion model-based planning for safety-critical robotic applications.
• To formally embed specification compliance—particularly safety constraints—into the diffusion generation process.
• To overcome the challenge of applying control barrier functions (CBFs) in diffusion models, which are not directly tied to system dynamics.
• To mitigate local trap problems in planning by incorporating time-varying invariance constraints into the diffusion process.
• To preserve the generalization and performance of diffusion models while enforcing safety through a quadratic program-based correction mechanism.

Proposed method

• Proposes a novel notion of finite-time diffusion invariance, ensuring trajectories remain within a safe set throughout the entire denoising process.
• Integrates control barrier functions (CBFs) into the diffusion time horizon to enforce forward invariance of the safe set.
• Modifies the denoising step using a quadratic program (QP) to project the predicted trajectory onto the feasible set defined by CBFs, preserving generative performance.
• Applies receding horizon control with diffusion-based path generation, enabling incremental, safe trajectory computation.
• Uses Lyapunov-based analysis to formally verify that the diffusion process remains invariant to safety constraints at the end of the denoising sequence.
• Employs time-dependent CBFs to handle dynamic constraints and avoid local traps in complex planning environments.

Experimental results

Research questions

• RQ1 Can diffusion probabilistic models be formally guaranteed to generate only safe trajectories in robotic planning tasks?
• RQ2 How can control barrier functions (CBFs) be effectively integrated into the diffusion time process, where no direct system dynamics are available?
• RQ3 Can finite-time diffusion invariance be achieved without sacrificing the generalization and sample quality of standard diffusion models?
• RQ4 How can local trap problems in planning be mitigated by embedding time-varying invariance constraints into the diffusion process?
• RQ5 What is the performance trade-off between safety guarantees and generative fidelity in diffusion-based planning?

Key findings

• SafeDiffuser successfully generates safe trajectories in all tested tasks—maze navigation, legged robot locomotion, and 3D space manipulation—without violating safety constraints.
• The method achieves formal safety guarantees through finite-time diffusion invariance, ensuring trajectories remain within the safe set at every denoising step.
• Quantitative evaluation shows that SafeDiffuser maintains high trajectory quality and generalization performance comparable to vanilla diffusion models, despite safety constraints.
• The integration of CBFs via a quadratic program preserves the model’s ability to explore diverse path spaces while enforcing safety.
• In comparison to standard diffusers, SafeDiffuser demonstrates significantly reduced failure rates in safety-critical environments, such as mazes with narrow passages.
• The approach is generalizable and applicable beyond robotics, with potential for use in image generation to ensure desired object patterns are consistently produced.