Diffusion-Guided Search via Exponential Tilting (DiffTilt): An Application to Falsification of Safety-Critical Systems

2026-07-25

AI Summary

This work addresses the challenge of detecting safety-critical failures in autonomous and cyber-physical systems, which arise from the joint rarity of environmental conditions and execution trajectories. To tackle this, the authors propose DiffTilt, a novel framework that uniquely integrates diffusion models with exponential tilting to enable efficient failure search via importance sampling. Without requiring an exact system model, DiffTilt leverages diffusion models to generate a joint prior over environment-execution pairs and incorporates an adaptive scoring function with specification-guided mechanisms. The approach provides theoretically grounded improvements in the efficiency of failure probability estimation, outperforming conventional conditional sampling strategies. Empirical evaluations on the ARCH-COMP benchmarks and a newly introduced articulated truck benchmark demonstrate significant gains over state-of-the-art methods, particularly in scenarios involving non-STL specifications.

Abstract

Discovering rare safety-critical failures in autonomous and cyber-physical systems is a fundamental challenge in verification and validation. Existing falsification approaches rely on conditional sampling strategies that factor the joint distribution over environments and system executions, and therefore suffer from multiplicative rarity effects: the simultaneous scarcity of failure-inducing inputs and failure-inducing traces makes exhaustive search prohibitively expensive. This paper develops DiffTilt, a distributional framework that exponentially tilts a diffusion model-induced joint distribution over environments and executions. We show that diffusion-guided sampling admits an exact interpretation as importance sampling in the joint space, where guidance scores induce a KL-optimal reallocation of probability mass towards failure-relevant behaviors. We further show that tilting provably amplifies failure probability and strictly outperforms conditional sampling, which is limited by multiplicative rarity. In this framework, the joint generative model serves as a reusable prior over scenarios and need not faithfully represent the system under test. Expensive system simulations are instead limited to learning a scoring function that characterizes scenario quality, enabling their selective and adaptive use. We study DiffTilt on ARCH-COMP benchmarks, and we propose an additional tractor-trailer benchmark showing the behavior of several approaches when scenario generation is guided by a well-defined specification rather than a reward. The proposed method achieves competitive or improved falsification performance compared to state-of-the-art approaches, with larger gains when specification definition is not limited to STL formulas.

Problem

• falsification
• safety-critical systems
• rare event
• multiplicative rarity
• autonomous systems

Innovation

• diffusion-guided search
• exponential tilting
• importance sampling
• falsification
• safety-critical systems