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.
Methods for discovering rare failures in autonomous systems have so far been demonstrated almost exclusively in simulations with simple, academic driving stacks, leaving open whether they generalize to the more robust planners used in commercial systems. We address this gap by applying two rare-event discovery algorithms to a commercial autonomous trucking stack. Adaptive stress testing (AST) uses reinforcement learning to search for the most likely noise trajectories leading to a simulated collision, while diffusion-based failure sampling (DiFS) trains a denoising diffusion model to sample a diverse set of failures. We show that both algorithms find simulated collisions during merge and cut-in maneuvers where traditional Monte Carlo simulation does not. To make these failures actionable, we introduce a statistical analysis based on principal component analysis (PCA) that classifies failures into common modes and identifies the timesteps that most influence the outcome. We cluster the principal components and invert the PCA transform to recover generalized noise trajectories, and show that these trajectories reproduce failures in identical and similar scenarios. This provides a path from failure discovery to systematic diagnosis of perception-level flaws.
In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a certified backup policy to ensure safety. To handle arbitrary uncertainties from ambiguous distributions, i.e., where the distribution is not of specific structure and the true distribution is unknown, we adopt a distributionally robust (DR) formulation using Wasserstein ambiguity sets. Rather than solving a high-dimensional DR trajectory optimization problem online, we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold. We validate our method through simulations across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet, demonstrating the broad applicability and computational efficiency.
Simulation-based testing of autonomous driving systems (ADS) must uncover realistic and diverse failures in dense, heterogeneous traffic. However, existing search-based seeding methods (e.g., genetic algorithms) struggle in high-dimensional spaces, often collapsing to limited modes and missing many failure scenarios. We present PtoP, a framework that combines adaptive random seed generation with Stein Variational Gradient Descent (SVGD) to produce diverse, failure-inducing initial conditions. SVGD balances attraction toward high-risk regions and repulsion among particles, yielding risk-seeking yet well-distributed seeds across multiple failure modes. PtoP is plug-and-play and enhances existing online testing methods (e.g., reinforcement learning--based testers) by providing principled seeds. Evaluation in CARLA on two industry-grade ADS (Apollo, Autoware) and a native end-to-end system shows that PtoP improves safety violation rate (up to 27.68%), scenario diversity (9.6%), and map coverage (16.78%) over baselines.