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This paper introduces DireSMC, a sequential Monte Carlo scheme designed to efficiently estimate the probability of rare events in diffusion models, which are often used as surrogates for expensive simulators. By guiding a population of weighted samples towards the target rare event using an analytical relaxation of the event set, DireSMC provides both samples and calibrated probability estimates. The method achieves significant speed-ups (9x to 1413x) over standard Monte Carlo methods on a climate emulator, accurately estimating probabilities down to $10^{-5}$.
Rare event probabilities in diffusion models can now be estimated orders of magnitude faster, unlocking their use in high-stakes scientific simulation.
Diffusion models are increasingly used as surrogates for expensive simulators in weather prediction, molecular dynamics, and materials design. In these models, computing the probability $p_0[E]$ of an event $E$ is difficult, especially when the event of interest is rare. A stable estimate using Monte Carlo becomes computationally intractable, requiring a growing sample size $\propto\!1/p_0[E]$ to compensate for an increasing rarity. In this paper, we present Diffusion Importance Sampling of Rare Events or DireSMC, a sequential Monte Carlo scheme that guides a population of weighted samples towards the rare event, giving access not only to samples but also to a calibrated estimate of its probability. We set up our guidance using an analytical relaxation of the event set, allowing the method to easily extend to a wide range of user-defined rare events. We validate our method on a toy problem with analytical solutions and on a score-based climate emulator, where we obtain accurate rare-event probabilities on a range of rarities from $10^{-3}$ to $10^{-5}$, achieving net speed-ups of $9\times$ to $1413\times$ over Monte Carlo.
