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 p0[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 ∝ 1/p0[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× to 1413× over Monte Carlo.
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BibTeX
@misc{subedi2026steering,
title = {{Steering Diffusion Models to Rare Events with Sequential Monte Carlo}},
author = {Aavash Subedi and Tim Reichelt and Christopher Williams and Philip Stier and Yee Whye Teh and Saifuddin Syed},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08652},
eprint = {2610.08652},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08652},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Steering Diffusion Models to Rare Events with Sequential Monte Carlo
AU - Aavash Subedi
AU - Tim Reichelt
AU - Christopher Williams
AU - Philip Stier
AU - Yee Whye Teh
AU - Saifuddin Syed
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.08652
UR - https://arxiv.org/abs/2610.08652
AB - 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 ∝ 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× to 1413× over Monte Carlo.
ER -