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

Miguel Espinosa; Eva Gmelich Meijling; Valerio Marsocci; Elliot J. Crowley; Mikolaj Czerkawski

cs.CVMar 3, 2026

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

Authors: Miguel Espinosa, Eva Gmelich Meijling, Valerio Marsocci, Elliot J. Crowley, Mikolaj Czerkawski

Organizations: School of Engineering, University of Edinburgh · European Space Agency (ESA) · Asterisk Labs

Abstract

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

Figures & tables

Figure 1: Conditional generation of Sentinel-2 L2A imagery from topography (DEM) and land-cover (LULC) inputs. We condition COP-GEN generations on DEM and LULC inputs (geographic location is provided solely for visual reference). COP-GEN produces diverse and physically consistent outputs, demonstrating variability in spectral appearance, illumination, and atmospheric conditions while preserving topographic and land-cover constraints. This highlights the model’s ability to capture the inherent one-to-many relationships of multimodal Earth Observation data. LULC classes are visualized using the following color scheme: Water , Trees , Flooded vegetation , Crops , Built-up areas , Bare ground , Snow/ice , Clouds , and Rangeland . Additional qualitative results and visualisations are provided in the Supplementary Material.

Year	Name	Modalities	Stochastic	Application
2023	GYOS	OSM, ArcGIS World Imagery	✓	Map-to-Optical
2023	DiffusionSat	S2, High-res RGB, lat-lon, GSD, cloud cover, timestamp, text	✓	General-purpose
2025	MESA	S2L2A, COP-DEM-30, text	✓	Text-to-Terrain
2025	COP-GEN-Beta	S2L2A (thumbnails), S2L1C (thumbnails) S1RTC (thumbnails), COP-DEM-30 (thumbnails)	✓	General-purpose
2025	TerraMind	S2L2A, S2RGB, S2L1C, S1RTC, S1GRD, NDVI, COP-DEM-30 LULC, lat-lon, image caption	✗	General-purpose
2025	COP-GEN	S2L2A, S2L1C, S1RTC, COP-DEM-30 LULC, timestamp, lat-lon	✓	General-purpose

Table 1: Overview of recent generative models for medium-resolution (10 m) Earth observation data. The table compares representative generative and multimodal models by year, supported input modalities, whether they explicitly model stochasticity, and their primary application scope. COP-GEN extends prior work by enabling stochastic generation across multiple Copernicus sensors within a unified general-purpose framework.

Figure 2: COP-GEN architecture, training, and inference overview. Multimodal inputs (optical, radar, elevation, land-cover, geolocation, and timestamps) are encoded into latent representations using modality-specific VAEs (or directly tokenized for scalar inputs). All tokens, augmented with modality-specific diffusion timestep embeddings, are processed by a shared transformer diffusion backbone. The model is trained to jointly predict noise for all modalities. At inference, modalities can be either sampled from noise or fixed at timestep zero, enabling both unconditional generation and flexible any-to-any conditional translation across modalities.

Source	Bands / Data	Res	Patches	Latent
S2L2A	B4,3,2,8	10m	$192\times 192$	$24\times 24$
	B5,6,7,8A,11,12	20m	$96\times 96$	$12\times 12$
	B1,9	60m	$32\times 32$	$4\times 4$
S2L1C	B3,2,8	10m	$192\times 192$	$24\times 24$
	B5,6,7,8A,11,12	20m	$96\times 96$	$12\times 12$
	B1,9,10	60m	$32\times 32$	$4\times 4$

Table 2: Data configuration and tokenization . Overview of input data sources, spectral bands, spatial resolutions, patch sizes, and corresponding latent grid dimensions used by the model. Multi-resolution Sentinel-2 imagery is patchified and encoded at resolution-specific latent scales, while geolocation and temporal metadata are embedded as global tokens.

Figure 3: Geospatial Distribution Analysis. We predict latitude–longitude coordinates conditioned on DEM and LULC inputs ( $n=50$ runs). TerraMind ( blue ) collapses to a few locations, whereas COP-GEN ( green ) predicts a distribution of plausible locations that share similar topographic and biome characteristics, accurately reflecting the non-injective nature of the mapping. A Köppen–Geiger climate classification basemap is overlaid to provide climatic context for the predicted locations. The ground-truth acquisition location is indicated by a red star ( ${\color[rgb]{1,0,0}\bigstar}$ ), and real thumbnail visualisations of the predicted locations are shown for comparison.

Figure 4: Distribution spread narrowing by progressively increasing input conditioning. As additional modalities are provided as input, the generated samples better align with the ground-truth (GT) distribution. For each conditioning setup, we generate 25 stochastic samples of Sentinel-2 L2A (S2L2A) imagery and report the predicted band distributions using histograms and kernel density estimates (KDEs). One spectral band is selected per S2L2A spatial resolution. The legend indicates the set of input modalities used for conditioning, always for a fixed geographic tile (215U_1019R). Additional bands and visualisations are provided in the appendix.

Figure 5: Per-pixel spectral reflectance profiles across multiple LULC classes. Conditioned on DEM and LULC inputs, COP-GEN generates multispectral S2L2A imagery that captures physically consistent spectral relationships. The plots compare spectral profiles from selected pixel locations in both real and generated images across the Sentinel-2 bands. The close alignment for trees, bare soil, water, crops, built-up areas, etc. demonstrates the model’s ability to accurately reconstruct characteristic land-cover responses. Geographical location is provided for reference. Additional visualisations are provided in Supplementary Material.

Figure 6: Band infilling via resolution-specific latent groups. By grouping Sentinel-2 bands according to resolution, COP-GEN treats spectral groups as independent modalities. Here, the model is conditioned only on the high-resolution visible band group (B2, B3, B4, B8) and successfully reconstructs the remaining spectral bands, auxiliary sensors (S1RTC, DEM), LULC maps, cloud mask, timestamp, and location. The high fidelity of the generated bands demonstrates effective cross-band and cross-modal inference. Geographical location thumbnail is provided for reference only.

		Peak perf. (Best per Tile)
Target	Metric	COP-GEN	TerraMind
DEM	MAE $\downarrow$	26.80	145.62
DEM	SSIM $\uparrow$	0.45	0.44
LULC	Top-1 $\uparrow$	0.84	0.80
LULC	mIoU $\uparrow$	0.42	0.55
S1RTC	MAE $\downarrow$	2.63	2.64

Table 3: Tile-Level Peak Capability Analysis. We report the oracle performance (best generation selected per tile) to demonstrate the upper bound of generation quality. This metric isolates the model’s peak capability from stochastic variance. Bold indicates the best result. † indicates that S2L2A is not present among the input modalities. ‡ indicates that S2L1C is not present among the input modalities.

			COP-GEN	TerraM
Target	Removed	Metric	Best	Best
DEM	w/o LatLon	MAE $\downarrow$	47.44	140.01
	w/o LULC	MAE $\downarrow$	46.96	140.80
	w/o S1RTC	MAE $\downarrow$	54.85	140.86
	w/o S2L1C	MAE $\downarrow$	51.85	146.00
	w/o S2L2A	MAE $\downarrow$	45.78	146.71

Table 4: Tile-Level Summarized Best Performance (Leave-One-Out). We compare the peak performance of COP-GEN against TerraMind across all modalities. COP-GEN shows clear dominance in DEM reconstruction (MAE) and Optical bands (S2L1C/S2L2A), while TerraMind demonstrates stronger localization capabilities (LatLon).

Stream	Metric	COP-GEN	TerraMind
Spectral	1-NN accuracy $\downarrow$	0.911 $\pm$ 0.075	0.985 $\pm$ 0.027
	Precision ( $k{=}5$ ) $\uparrow$	0.289 $\pm$ 0.348	0.483 $\pm$ 0.469
	Recall ( $k{=}5$ ) $\uparrow$	0.900 $\pm$ 0.264	0.028 $\pm$ 0.080
	Intra-set distance	0.455 $\pm$ 0.155	0.050 $\pm$ 0.015
RGB	1-NN accuracy $\downarrow$	0.982 $\pm$ 0.031	0.998 $\pm$ 0.009
	Precision ( $k{=}5$ ) $\uparrow$	0.086 $\pm$ 0.220	0.119 $\pm$ 0.286

Table 5: Stochastic benchmark: COP-GEN vs. TerraMind across 489 cells, with 16 samples per cell for all three sources (real, COP-GEN, TerraMind). Mean

\pm

std reported. For 1-NN accuracy and MMD, lower is better (

\downarrow

); for Precision, Recall, and Coverage, higher is better (

\uparrow

). Intra-set distance is a diversity measure (higher indicates more diverse sets). Best values in bold .

Appendix figures & tables26 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Multiple conditional Sentinel-2 L2A generations from DEM and LULC inputs. Generated outputs per scene demonstrates COP-GEN’s ability to model multimodal variability in spectral response, illumination, and atmospheric conditions, while maintaining consistency with underlying terrain and land-cover information.

Figure 8: Conditional generation of Sentinel-2 L2A imagery from DEM and LULC inputs. For each location, a grid of generated examples illustrates the diversity of COP-GEN outputs under varying spectral, illumination, and atmospheric conditions, while respecting topographic and land-cover constraints. This demonstrates the model’s ability to represent one-to-many relationships in multimodal Earth observation.

Figure 9: Per-pixel spectral reflectance profiles across multiple LULC classes (560U_34R tile). The COP-GEN model reproduces characteristic Sentinel-2 band signatures for LULC classes, indicating robust learning of physical spectral patterns.

Figure 10: Per-pixel spectral reflectance profiles across multiple LULC classes (502U_263R tile). COP-GEN closely matches Sentinel-2 band responses, indicating physically meaningful spectral signatures across land-cover types.

Figure 11: Per-pixel spectral reflectance profiles across multiple LULC classes (256U_1125L tile). COP-GEN preserves characteristic Sentinel-2 spectral responses, illustrating consistent physical fidelity across land-cover types.

			COP-GEN		TerraMind
Target	Condition (Input)	Metric	Mean $\pm$ Std	Best	Mean $\pm$ Std	Best
DEM	Full Context	MAE $\downarrow$	301.79 $\,\pm$ 260.49	26.80	159.96 $\,\pm$ 515.97	145.62
		RMSE $\downarrow$	304.05 $\,\pm$ 261.26	30.72	161.66 $\,\pm$ 516.68	147.54
		SSIM $\uparrow$	0.18 $\,\pm$ 0.15	0.45	0.37 $\,\pm$ 0.31	0.44
LULC	Full Context	Top-1 Acc $\uparrow$	0.52 $\,\pm$ 0.18	0.84	0.78 $\,\pm$ 0.30	0.80
		Mean IoU $\uparrow$	0.19 $\,\pm$ 0.10	0.42	0.46 $\,\pm$ 0.28	0.55

Appendix

Table 6: Tile-Level Cross-Modal Generation Analysis. We sample 36 times per tile. We report the performance of COP-GEN and TerraMind across all tiles. Mean denotes the average performance across all seeds and tiles (measuring stability), while Best denotes the oracle selection of the best generation per tile (measuring peak capability). The “Condition” column indicates the available input modalities. Bold indicates the best result between the two models for a given metric/setting.

Model	Conditioning Variant	MAE $\downarrow$	RMSE $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$
Target: Digital Elevation Model (DEM)
COP-GEN	All-minus-target	301.79 $\,\pm$ 9.48	483.21 $\,\pm$ 20.54	0.18 $\,\pm$ 0.01	5.79 $\,\pm$ 0.10
TerraMind	All-minus-target	159.96 $\,\pm$ 1.57	542.53 $\,\pm$ 12.51	0.37 $\,\pm$ 0.00	7.83 $\,\pm$ 0.05
Target: Sentinel-1 (S1RTC)
COP-GEN	All-minus-target	3.48 $\,\pm$ 0.05	4.67 $\,\pm$ 0.16	0.10 $\,\pm$ 0.00	14.24 $\,\pm$ 0.08
TerraMind	All-minus-target	2.74 $\,\pm$ 0.00	3.63 $\,\pm$ 0.01	0.17 $\,\pm$ 0.00	18.28 $\,\pm$ 0.02

Appendix

Table 7: Experiment-Level Cross-Modal Generation Performance. We generate a single sample per tile, and obtain a final aggregated test metric. We run 36 times and report mean and std. Comparison of COP-GEN vs. TerraMind. For distinct modalities, we report domain-specific metrics. All-minus-target implies all available modalities are used as conditioning. Bold indicates the best result.

			COP-GEN		TerraMind
Target	Removed Modality	Metric	Mean $\pm$ Std	Best	Mean $\pm$ Std	Best
DEM	w/o LatLon	MAE $\downarrow$	308.65 $\,\pm$ 280.81	47.44	164.01 $\,\pm$ 546.39	140.01
	w/o LatLon	SSIM $\uparrow$	0.18 $\,\pm$ 0.16	0.41	0.40 $\,\pm$ 0.28	0.53
	w/o LULC	MAE $\downarrow$	305.07 $\,\pm$ 271.09	46.96	163.98 $\,\pm$ 545.79	140.80
	w/o LULC	SSIM $\uparrow$	0.17 $\,\pm$ 0.16	0.40	0.40 $\,\pm$ 0.28	0.53
	w/o S1RTC	MAE $\downarrow$	318.17 $\,\pm$ 281.35	54.85	164.12 $\,\pm$ 541.42	140.86

Appendix

Table 8: Extended Leave-One-Out Ablation Analysis (Tile-Level). We analyze the impact of removing individual modalities on generation performance across all combinations. We report MAE and PSNR for all continuous bands. COP-GEN demonstrates superior peak performance (“Best” column) across DEM and optical tasks, significantly outperforming TerraMind in MAE when correlated modalities are present.

	MAE $\downarrow$		RMSE $\downarrow$		SSIM $\uparrow$		PSNR $\uparrow$
Removed	COP-GEN	Terra.	COP-GEN	Terra.	COP-GEN	Terra.	COP-GEN	Terra.
Target: Digital Elevation Model (DEM)
Lat/Lon	308.65 $\,\pm$ 14.85	164.01 $\,\pm$ 4.38	500.39 $\,\pm$ 30.78	574.52 $\,\pm$ 35.96	0.18 $\,\pm$ 0.01	0.40 $\,\pm$ 0.03	5.73 $\,\pm$ 0.09	7.83 $\,\pm$ 0.05
LULC	305.07 $\,\pm$ 10.36	163.98 $\,\pm$ 4.70	493.47 $\,\pm$ 24.48	573.99 $\,\pm$ 37.49	0.17 $\,\pm$ 0.01	0.40 $\,\pm$ 0.03	5.78 $\,\pm$ 0.10	7.82 $\,\pm$ 0.05
S1RTC	318.17 $\,\pm$ 10.19	164.12 $\,\pm$ 3.75	513.10 $\,\pm$ 17.68	569.83 $\,\pm$ 32.49	0.18 $\,\pm$ 0.00	0.40 $\,\pm$ 0.03	5.71 $\,\pm$ 0.11	7.74 $\,\pm$ 0.05
S2L1C	434.98 $\,\pm$ 16.66	172.71 $\,\pm$ 3.38	762.06 $\,\pm$ 38.21	571.05 $\,\pm$ 31.62	0.17 $\,\pm$ 0.01	0.39 $\,\pm$ 0.02	5.59 $\,\pm$ 0.10	7.59 $\,\pm$ 0.05

Appendix

Table 9: Leave-One-Out Ablation Performance. Experiment-level. Comparison of COP-GEN vs. TerraMind (Terra.) when removing a single input modality. We report Mean

\pm

Std. Bold indicates the best result between the two models.

	TerraMind (Base)	COP-GEN (Base)
Backbone Parameters	237.62 M	286.99 M

Appendix

Table 10: Backbone parameter comparison. Number of trainable parameters in the base backbone architectures of TerraMind and COP-GEN. COP-GEN achieves multimodal stochastic generation and any-to-any conditional modeling with a parameter count comparable to existing Earth observation foundation models.

Figure 12: Geospatial distribution analysis. Latitude–longitude coordinates are predicted from DEM and LULC inputs over $n=50$ runs. TerraMind ( blue ) collapses to a small set of locations, whereas COP-GEN ( green ) produces a broader distribution of plausible sites sharing similar topographic and biome characteristics, reflecting the non-injective nature of the mapping. Real thumbnail visualisations of predicted locations are shown for reference.

Figure 13: Geospatial distribution analysis. Conditional latitude–longitude predictions from DEM and LULC inputs ( $n=50$ ) reveal that TerraMind ( blue ) concentrates on a few modes, while COP-GEN ( green ) captures multiple plausible geographic locations with similar terrain and biome properties, consistent with a non-injective mapping. Example real-image thumbnails are provided for comparison.

Figure 14: Geospatial distribution analysis. Given DEM and LULC inputs, latitude–longitude predictions over $n=50$ runs show TerraMind ( blue ) collapsing to a limited set of locations, while COP-GEN ( green ) captures a diverse distribution of plausible sites with similar topographic and biome characteristics, reflecting the non-injective nature of the task. This behavior is further supported by the fact that most COP-GEN predictions fall within the Arid Köppen–Geiger climate class, consistent with the bare-ground input. Real location thumbnails are shown for reference.

Figure 15: Geospatial distribution analysis. We evaluate conditional latitude–longitude prediction from DEM and LULC inputs across $n=50$ samples. TerraMind ( blue ) tends to collapse to a few specific locations, whereas COP-GEN ( green ) generates a spatially distributed set of plausible locations with similar terrain and biome attributes, consistent with a non-injective mapping. Real thumbnail visualizations of predicted locations are included.

Figure 16: Effect of input conditioning on spectral distribution spread (195D_669L). As additional input modalities are incorporated, generated samples increasingly align with the ground-truth (GT) distribution. For each conditioning configuration, 25 stochastic Sentinel-2 L2A (S2L2A) samples are generated, and predicted band distributions are summarized using histograms and kernel density estimates (KDEs).

Figure 17: Effect of input conditioning on spectral distribution spread (248U_978R). Increasing the number of conditioning modalities progressively constrains the generated Sentinel-2 L2A (S2L2A) outputs toward the ground-truth (GT) distribution. For each setting, 25 stochastic samples are generated and evaluated using histograms and kernel density estimates (KDEs).

Figure 18: Effect of input conditioning on spectral distribution spread (250U_409R). As additional modalities are used for conditioning, the variability of generated Sentinel-2 L2A (S2L2A) samples decreases and better matches the ground-truth (GT) distribution. For each configuration, 25 stochastic generations are summarized via histograms and kernel density estimates (KDEs).

Figure 19: Effect of input conditioning on spectral distribution spread (143D_1481R). Providing additional conditioning modalities narrows the distribution of generated Sentinel-2 L2A (S2L2A) samples toward the ground truth. For each setup, 25 stochastic samples are evaluated using histograms and KDEs.

Figure 20: Class-conditional geolocation priors for trees. COP-GEN is conditioned solely on a land-cover tile that is entirely labeled as trees . The model generates multiple plausible latitude–longitude samples, which are plotted as points on the map. The background shows global tree cover, normalised by percentage, where darker green indicates higher tree density. Predicted locations concentrate in regions with substantial forest cover across multiple continents, indicating that COP-GEN has learned meaningful global geographic priors associated with tree-dominated landscapes, with limited dispersion into implausible regions.

Figure 21: Class-conditional geolocation priors for snow and ice. The model is conditioned on a tile fully assigned to the snow/ice land-cover class and outputs multiple plausible latitude–longitude samples. Predictions are overlaid on a global mountain-range basemap to provide geographic context. The majority of samples align with high-latitude and high-elevation regions, including the Himalayas, Alaska, Patagonia, and other major mountain systems, demonstrating that COP-GEN captures realistic geographic and topographic priors associated with persistent snow and ice cover.

Figure 22: Class-conditional geolocation priors for rangeland. COP-GEN is conditioned on a homogeneous rangeland tile and generates a distribution of plausible geographic locations. The predictions are visualised on a Köppen–Geiger climate classification basemap. Generated locations predominantly fall within arid climate zone and exhibit broad global coverage, indicating that the model has learned large-scale climatic associations characteristic of rangeland ecosystems.

Figure 23: Class-conditional geolocation priors for flooded vegetation. Given a tile entirely labeled as flooded vegetation , COP-GEN outputs multiple candidate latitude–longitude samples. Predictions are plotted on a global tree cover basemap (normalised by percentage) to contextualise vegetation density. The predicted locations tend to cluster in forested and wetland-rich regions, consistent with the ecological conditions under which flooded vegetation typically occurs, while maintaining reasonable geographic diversity.

Figure 24: Class-conditional geolocation priors for crops. The model is conditioned on a land-cover tile fully classified as crops and produces multiple plausible geographic locations. Predictions are overlaid on a Köppen–Geiger climate basemap. Samples concentrate in temperate and continental climate zones, with notable densities over Central Europe, North America, and Central Asia. The inferred latitude distribution aligns well with known climatic requirements for large-scale agriculture, indicating that COP-GEN captures meaningful agro-climatic priors.

Figure 25: Class-conditional geolocation priors for clouds. COP-GEN is conditioned on a tile entirely labeled as clouds and generates multiple latitude–longitude predictions. The points are visualised on a global mountain-range basemap. Many samples align with major orographic regions such as the Himalayas and the Andes, where cloud formation is frequent due to topographic lifting, suggesting that the model has learned physically plausible geographic patterns associated with persistent cloud cover.

Figure 26: Class-conditional geolocation priors for built-up areas. Conditioned on a homogeneous built-up land-cover tile, COP-GEN generates a distribution of plausible geographic locations. Predictions are overlaid on a global population density basemap. The model places most samples in densely populated regions, particularly across Asia, with additional concentrations in Europe and North America, reflecting realistic global settlement patterns and urbanisation priors.

Figure 27: Class-conditional geolocation priors for bare ground. Given a tile fully classified as bare ground , COP-GEN outputs multiple candidate latitude–longitude locations. Predictions are shown on a Köppen–Geiger climate basemap. The majority of samples fall within arid climate zones and are broadly distributed across global desert regions, aligning well with the expected geographic distribution of bare soil and sparsely vegetated landscapes.

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