Diffusion models are increasingly used as cheap stand-ins for costly simulators in areas like weather and materials. But estimating the probability that a rare event happens under these models is hard. A plain Monte Carlo approach needs about 1/p samples when the true probability is p, so it becomes infeasible as events get rarer. The paper introduces Diffusion Importance Sampling of Rare Events, or DireSMC, to address this gap.

The authors design a Sequential Monte Carlo (SMC) procedure that works with diffusion-model surrogates. Rather than drawing many independent samples at random, DireSMC keeps a population of weighted samples and progressively steers them toward the rare event of interest. The method uses an analytical relaxation of the event set to build that guidance. Because samples carry weights, the algorithm can both produce examples of the rare event and give a calibrated estimate of its probability.

At a high level, DireSMC combines two familiar ideas. Importance sampling focuses computational effort where the event is more likely to occur. Sequential Monte Carlo moves and reweights a population of particles over time to approximate a target distribution. The paper sets up the guidance signals for those movements using a softened, analytic version of the event definition. That choice is what lets the same approach handle many kinds of user-defined rare events.

The authors tested the method on a toy problem with known analytic answers and on a score-based climate emulator, a diffusion-model surrogate for climate simulations. On the climate emulator they report accurate probability estimates for events with true probabilities between 10^-3 and 10^-5. Compared with straightforward Monte Carlo, they report net speed-ups ranging from about 9× up to 1,413×, depending on how rare the event was.