# Extreme Event Likelihoods with Guided Generative Models

[NVIDIA Developer Blog](https://yomu.fyi/company/nvidia-developer-blog) · Elizabeth Goodman · Jul 13, 2026

**Type:** Explainer

## Summary

Estimating the likelihood of extreme, high-impact events using brute-force Monte Carlo simulations requires excessive model iterations for expensive physics-based climate models. While guided diffusion models steer generation toward rare events like tropical cyclones, oversampling distorts the true probability distribution. To address this, researchers guide the diffusion-based climate emulator NVIDIA cBottle toward specific events and compute log-odds ratios between guided and unguided distributions. Reweighting the guided samples via these odds ratios enables importance sampling under the original climate distribution. Implemented in NVIDIA Earth2Studio, this technique reduced standard error by 25% compared to simple Monte Carlo sampling when evaluating tropical cyclone states.

## Context

Estimating rare, high-impact climate events like tropical cyclones via brute-force Monte Carlo sampling requires large simulation ensembles, creating a bottleneck for risk analysis. Steering diffusion models toward rare events oversamples distribution tails, distorting the original probability.

## Approach / What changed

Using NVIDIA cBottle in Earth2Studio, researchers steer a diffusion model toward tropical cyclone states and compute the log-odds ratio between unguided and guided probabilities. This ratio acts as an importance sampling weight to estimate true likelihoods under the base distribution.

## Takeaways

- The odds-ratio calculation requires estimating generative flow divergence, which needs second-order derivatives through the diffusion model.
- Combining guided generation with odds-ratio reweighting reduced standard error by 25% compared to simple Monte Carlo sampling in tropical cyclone cases.
- A negative log-odds ratio indicates that the generated sample is substantially more likely under the guided distribution than under the unguided base model.

**Tags:** [Machine Learning](https://yomu.fyi/topic/machine-learning), [Open Source](https://yomu.fyi/topic/open-source), [Python](https://yomu.fyi/topic/python)

[Read original post](https://developer.nvidia.com/blog/extreme-event-likelihoods-with-guided-generative-models)