# Steering Diffusion Models to Rare Events with Sequential Monte Carlo

arXiv: https://arxiv.org/abs/2610.08652 · HTML: https://mlsanity.com/paper/2610.08652/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 8 of its 99 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo](https://mlsanity.com/paper/2502.12786/) (2025)
- [Enhanced Diffusion Sampling: Efficient Rare Event Sampling and Free Energy Calculation with Diffusion Models](https://mlsanity.com/paper/2602.16634/) (2026)
- [Metropolis-Adjusted Diffusion Models](https://mlsanity.com/paper/2605.09654/) (2026)
- [Towards accurate extreme event likelihoods from diffusion model climate emulators](https://mlsanity.com/paper/2605.03802/) (2026)

## Abstract (arXiv)

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 propto!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.