# Conditional Diffusion-Based Retrieval of Atmospheric CO2 from Earth Observing Spectroscopy

arXiv: https://arxiv.org/abs/2504.17074 · HTML: https://mlsanity.com/paper/2504.17074/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 23 Apr 2025.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)

## Built on by (most cited first, 1 of 1)

- [Amortized Probabilistic Retrieval of Atmospheric CO2 from OCO-2 Spectra Using Deep Learning with Laplace Approximations and Normalizing Flows](https://mlsanity.com/paper/2606.17413/) (2026)

## Abstract (arXiv)

Satellite-based estimates of greenhouse gas (GHG) properties from observations of reflected solar spectra are integral for understanding and monitoring complex terrestrial systems and their impact on the carbon cycle due to their near global coverage. Known as retrieval, making GHG concentration estimations from these observations is a non-linear Bayesian inverse problem, which is operationally solved using a computationally expensive algorithm called Optimal Estimation (OE), providing a Gaussian approximation to a non-Gaussian posterior. This leads to issues in solver algorithm convergence, and to unrealistically confident uncertainty estimates for the retrieved quantities. Upcoming satellite missions will provide orders of magnitude more data than the current constellation of GHG observers. Development of fast and accurate retrieval algorithms with robust uncertainty quantification is critical. Doing so stands to provide substantial climate impact of moving towards the goal of near continuous real-time global monitoring of carbon sources and sinks which is essential for policy making. To achieve this goal, we propose a diffusion-based approach to flexibly retrieve a Gaussian or non-Gaussian posterior, for NASA's Orbiting Carbon Observatory-2 spectrometer, while providing a substantial computational speed-up over the current operational state-of-the-art.