Efficient Rare-Event Estimation Can Distort Conditional Trajectories

Rare-event proposals can supply both probability estimates and trajectories used to explain how an event occurs. On a controlled diffusion, learning raises estimation efficiency, reduces estimated global conditional fidelity, and improves route-conditioned hitting-time accuracy on the same evaluation paths. This combination occurs in all five original models and all five new fits trained through the deployed control cap, with evaluation on fresh paths. RareFlow characterizes this separation through the exact factorization $S=HF$, where $H$ is event discovery and $F$ is the reciprocal of one plus the forward ${\chi }^2$ conditional discrepancy. A mechanism decomposition separates route allocation from within-route distortion. An independent guide-family comparison shows that nearly matched route shares can conceal timing bias, while an exact conditional-law ceiling limits what route reallocation alone can repair. A finite-state control exposes severe overestimation of this ceiling when an important submode receives sparse proposal coverage. A second planar landscape reproduces the qualitative discovery–fidelity separation. Together, these results show that improved probability estimation does not by itself certify faithful unweighted event trajectories, and that full conditional fidelity and observable-specific accuracy should be evaluated separately.