Steering Diffusion Models to Rare Events with Sequential Monte Carlo

2026-10-06

AI Summary

This study addresses the computational inefficiency and numerical instability inherent in rare event probability estimation within diffusion models. We propose DireSMC, a method integrating sequential Monte Carlo, importance sampling, and analytical relaxation techniques. By leveraging an analytically relaxed event set to establish a guiding mechanism, DireSMC efficiently drives weighted samples toward target regions while accommodating user-defined rare event specifications. This approach overcomes the efficiency limitations of standard Monte Carlo sampling, achieving both efficient sample generation and precise probability calibration. In climate simulator experiments, DireSMC accurately estimates extreme event probabilities on the order of $10^{-3}$ to $10^{-5}$, yielding 9- to 1413-fold speedups compared to conventional Monte Carlo methods.

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.

Problem

• Diffusion Models
• Rare Events
• Probability Estimation
• Monte Carlo
• Computational Intractability

Innovation

• Diffusion Models
• Sequential Monte Carlo
• Rare Event Sampling
• Importance Sampling
• Score-based Climate Emulator