# Towards accurate extreme event likelihoods from diffusion model climate emulators

arXiv: https://arxiv.org/abs/2605.03802 · HTML: https://mlsanity.com/paper/2605.03802/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 5 May 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, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses](https://mlsanity.com/paper/2411.11268/) (2024)
- [Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling](https://mlsanity.com/paper/2408.10958/) (2024)
- [Generative Data Assimilation of Sparse Weather Station Observations at Kilometer Scales](https://mlsanity.com/paper/2406.16947/) (2024)
- [GraphDOP: Towards skilful data-driven medium-range weather forecasts learnt and initialised directly from observations](https://mlsanity.com/paper/2412.15687/) (2024)
- [Joint Distillation for Fast Likelihood Evaluation and Sampling in Flow-based Models](https://mlsanity.com/paper/2512.02636/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting](https://mlsanity.com/paper/2601.18111/) (2026)
- [Learn to Guide Your Diffusion Model](https://mlsanity.com/paper/2510.00815/) (2025)
- [FALCON: Few-step Accurate Likelihoods for Continuous Flows](https://mlsanity.com/paper/2512.09914/) (2025)
- [Score-based generative emulation of impact-relevant Earth system model outputs](https://mlsanity.com/paper/2510.04358/) (2025)
- [Long-Range Distillation: Distilling 10,000 Years of Simulated Climate into Long Timestep AI Weather Models](https://mlsanity.com/paper/2512.22814/) (2025)

## Built on by (most cited first, 2 of 2)

- [Conditional Tropical Cyclogenesis Rates via Rare-Event Sampling in a Neural Weather Emulator](https://mlsanity.com/paper/2606.30920/) (2026)
- [Steering Diffusion Models to Rare Events with Sequential Monte Carlo](https://mlsanity.com/paper/2610.08652/) (2026)

## Abstract (arXiv)

ML climate model emulators are useful for scenario planning and adaptation, allowing for cost-efficient experimentation. Recently, the diffusion model Climate in a Bottle (cBottle) has been proposed for generation of atmospheric states compatible with boundary conditions of solar position and sea surface temperatures. Crucially, cBottle can be guided to generate extreme events such as Tropical Cyclones (TCs) over locations of interest. Diffusion models such as cBottle work by approximating the probability density of the training data. Here, we show use cases of the probability density estimates of atmospheric states obtained from this climate emulator. Most importantly, these estimates allow us to calculate likelihoods of extreme events under guidance. When guiding the model towards states including TCs, comparing the probability density under the guided and unguided model enables us to quantify how much more likely the guidance has made the TC. We show how these odds ratios allow us to importance-sample from the TC distribution, reducing the standard error of the probability estimate compared to simple Monte Carlo sampling. Furthermore, we discuss results and limitations of the application of model probability densities to extreme event attribution-like experiments. We present these early but encouraging results hoping they will spur more research into probabilistic information that can be gained from diffusion models of the atmosphere.