Steering Diffusion Models to Rare Events with Sequential Monte Carlo

Aavash Subedi, Tim Reichelt, Christopher Williams, Philip Stier, Yee Whye Teh +1

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 rare event sampling with Sequential Monte Carlo (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.