Steering Diffusion Models to Rare Events with Sequential Monte Carlo

Abstract: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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.08652 [stat.ML]

(or arXiv:2610.08652v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.08652 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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