# COP-GEN: Latent Diffusion Transformer for Copernicus Earth Observation Data

arXiv: https://arxiv.org/abs/2603.03239 · HTML: https://mlsanity.com/paper/2603.03239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 49 of its 73 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 49)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [All are Worth Words: A ViT Backbone for Diffusion Models](https://mlsanity.com/paper/2209.12152/) (2022)
- [SegDiff: Image Segmentation with Diffusion Probabilistic Models](https://mlsanity.com/paper/2112.00390/) (2021)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer](https://mlsanity.com/paper/2303.14389/) (2023)
- [One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale](https://mlsanity.com/paper/2303.06555/) (2023)
- [AlphaEarth Foundations: An embedding field model for accurate and efficient global mapping from sparse label data](https://mlsanity.com/paper/2507.22291/) (2025)
- [DiffusionSat: A Generative Foundation Model for Satellite Imagery](https://mlsanity.com/paper/2312.03606/) (2023)
- [TerraMind: Large-Scale Generative Multimodality for Earth Observation](https://mlsanity.com/paper/2504.11171/) (2025)
- [MMEarth: Exploring Multi-Modal Pretext Tasks For Geospatial Representation Learning](https://mlsanity.com/paper/2405.02771/) (2024)
- [OmniSat: Self-Supervised Modality Fusion for Earth Observation](https://mlsanity.com/paper/2404.08351/) (2024)
- [CRS-Diff: Controllable Remote Sensing Image Generation with Diffusion Model](https://mlsanity.com/paper/2403.11614/) (2024)
- [Galileo: Learning Global & Local Features of Many Remote Sensing Modalities](https://mlsanity.com/paper/2502.09356/) (2025)
- [MetaEarth: A Generative Foundation Model for Global-Scale Remote Sensing Image Generation](https://mlsanity.com/paper/2405.13570/) (2024)
- [SatSynth: Augmenting Image-Mask Pairs through Diffusion Models for Aerial Semantic Segmentation](https://mlsanity.com/paper/2403.16605/) (2024)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [Changen2: Multi-Temporal Remote Sensing Generative Change Foundation Model](https://mlsanity.com/paper/2406.17998/) (2024)
- [Joint Embedding vs Reconstruction: Provable Benefits of Latent Space Prediction for Self Supervised Learning](https://mlsanity.com/paper/2505.12477/) (2025)
- [Panopticon: Advancing Any-Sensor Foundation Models for Earth Observation](https://mlsanity.com/paper/2503.10845/) (2025)
- [Major TOM: Expandable Datasets for Earth Observation](https://mlsanity.com/paper/2402.12095/) (2024)
- [Generate Your Own Scotland: Satellite Image Generation Conditioned on Maps](https://mlsanity.com/paper/2308.16648/) (2023)

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

- [Now We Know? A Systematic Comparison of TerraMind and THOR](https://mlsanity.com/paper/2607.18504/) (2026)

## Abstract (arXiv)

Earth observation applications increasingly rely on data from multiple sensors, including optical, radar, elevation, and land-cover. Relationships between modalities are fundamental for data integration but are inherently non-injective: identical conditioning information can correspond to multiple physically plausible observations, and should be parametrised as conditional distributions. Deterministic models, by contrast, collapse toward conditional means and fail to represent the uncertainty and variability required for tasks such as data completion and cross-sensor translation. We introduce COP-GEN, a multimodal latent diffusion transformer that models the joint distribution of heterogeneous EO modalities at their native spatial resolutions. By parameterising cross-modal mappings as conditional distributions, COP-GEN enables flexible any-to-any conditional generation, including zero-shot modality translation without task-specific retraining. Experiments show that COP-GEN generates diverse yet physically consistent realisations while maintaining strong peak fidelity across optical, radar, and elevation modalities. Qualitative and quantitative analyses demonstrate that the model captures meaningful cross-modal structure and adapts its output uncertainty as conditioning information increases. We release a stochastic benchmark built from multi-temporal Sentinel-2 observations that enables distribution-level comparison of generative EO models. On this benchmark, COP-GEN covers 90% of the real observation manifold and 63% of its per-band reflectance range, while the strongest competing method collapses to 2.8% and 18%, respectively. These results highlight the importance of stochastic generative modeling for EO and motivate evaluation protocols beyond single-reference, pointwise metrics. Website: https://miquel-espinosa.github.io/cop-gen