SatSplatDiff: Diffusion-Enhanced Satellite Splatting

• SatSplatDiff is a diffusion-augmented Gaussian-splatting framework that integrates photogrammetric DSM initialization, monocular depth supervision, and 2D shadow casting to stabilize satellite 3D reconstruction.
• It employs a geometry-anchored generative loop where diffusion-refined pseudo-views are conditioned on shadow maps, ensuring that facade details and albedo enhancements remain tied to real-world geometry.
• The approach combines multi-scale geometric refinement with adaptive densification, achieving up to 5× effective resolution enhancement and significant improvements in both geometric accuracy and visual quality.

SatSplatDiff denotes a diffusion-augmented Gaussian-splatting framework whose clearest titled usage in the supplied literature is the satellite reconstruction method "SatSplatDiff: Geometry-preserving generative refinement for high-fidelity satellite Gaussian Splatting" (Kim et al., 25 Jun 2026). In that formulation, the method addresses a characteristic weakness of satellite 3D reconstruction: near-nadir imagery strongly supervises roofs and ground but weakly constrains façades, so naïve generative enhancement can improve appearance while damaging geometry. SatSplatDiff therefore combines photogrammetric DSM initialization, 2DGS-based shadow casting, monocular depth supervision, multi-scale geometric refinement, and shadow-guided generative refinement so that visual enhancement remains tied to geometry (Kim et al., 25 Jun 2026). In the supplied material, the same label is also used as a shorthand for a distinct single-image generative 3D completion method based on latent diffusion over Gaussian splats (Liao et al., 29 Aug 2025), making the term context-dependent.

1. Terminology and scope

In the supplied literature, "SatSplatDiff" has more than one usage. As a paper title, it names the satellite method for geometry-preserving generative refinement in 2D Gaussian Splatting for Earth observation scenes (Kim et al., 25 Jun 2026). Separately, the data for "Complete Gaussian Splats from a Single Image with Denoising Diffusion Models" describes that method as "SatSplatDiff: single-image, generative 3D scene completion with Gaussian splats," even though its paper title is different (Liao et al., 29 Aug 2025). This suggests that the label functions partly as a shorthand rather than a uniquely fixed bibliographic name.

The ambiguity is reinforced by adjacent papers. "High-Fidelity Novel View Synthesis via Splatting-Guided Diffusion" notes that SplatDiff is "often mis-searched as 'SatSplatDiff'" (Zhang et al., 18 Feb 2025). SkySplat explicitly states that its own paper does not mention "SatSplatDiff" (Huang et al., 13 Aug 2025). Splat4D uses the phrase only in a comparative section, "Connecting to 'SatSplatDiff': a diffusion-augmented Gaussian splatting pipeline," rather than as its method name (Yin et al., 11 Aug 2025). Accordingly, the term most usefully refers either to the satellite method of (Kim et al., 25 Jun 2026) or, in some summaries, to single-image generative Gaussian-splat completion (Liao et al., 29 Aug 2025); the two should not be conflated.

2. Satellite reconstruction problem and design objective

In the satellite setting, the central issue is viewpoint bias. Satellite imagery is predominantly acquired from near-nadir viewpoints, which yields dense supervision for rooftops and ground but sparse supervision for façades and other vertical structures. In Gaussian Splatting, this produces weak gradients on façades, surface holes, and low-resolution textures when scenes are viewed off-nadir (Kim et al., 25 Jun 2026). The same paper identifies a second failure mode in prior generative refinement pipelines: if diffusion-refined pseudo-views are generated independently per view, they can hallucinate plausible but incorrect textures, break photo-consistency, and pull geometry toward spurious appearance cues, a failure observed in Skyfall-GS (Kim et al., 25 Jun 2026).

SatSplatDiff is formulated to preserve geometric cues during visual enhancement. Its inputs are multi-date satellite images with RPC camera models and solar metadata, a photogrammetric DSM with bundle-adjusted cameras from ASP or s2p, and a monocular depth prior from Depth Anything V2, ViT-L (Kim et al., 25 Jun 2026). Its intermediate representations include 2DGS primitives as oriented disks, affine camera models approximating RPCs, geometry-derived shadow visibility masks, and diffusion-refined pseudo-views conditioned by shadow-cast renders (Kim et al., 25 Jun 2026). Its outputs are both geometric and photometric: a DSM rendered from 2DGS with well-regularized façade geometry, and high-fidelity, sensor-consistent albedo with shadow-aware renders, including up to $5\times$ effective resolution enhancement (Kim et al., 25 Jun 2026).

A useful way to characterize the method is as a geometry-anchored generative loop. Geometry is first stabilized by photogrammetric and monocular priors; only then are pseudo-views introduced, and those pseudo-views are conditioned by shadow maps computed from the current geometry. This differs from view-independent refinement, where appearance improvements may not remain compatible with the underlying 3D structure (Kim et al., 25 Jun 2026).

3. Representation, shadow casting, and geometric refinement

SatSplatDiff uses 2D Gaussian Splatting rather than unconstrained 3D volumetric rendering. The general Gaussian ingredients are mean $\mu_i \in \mathbb{R}^3$, covariance $\Sigma_i \in \mathbb{R}^{3 \times 3}$, color $c_i$, and opacity $\alpha_i$; screen-space density and front-to-back compositing follow the usual projected Gaussian form, with expected depth

$D_{\text{render}}(u) = \sum_{i=1}^{N} w_i(u) z_i.$

The actual method uses 2DGS oriented disks and exact ray-disk intersections for geometry-accurate rendering, with alpha blending written as

$$R(x) = \sum_{i=1}^{N} a_i \alpha_i \hat{G}_i(u(x)) \prod_{j=1}^{i-1} \left(1 - \alpha_j \hat{G}_j(u(x))\right),$$

where $a_i$ can be color, normal, or depth (Kim et al., 25 Jun 2026).

Initialization begins from a photogrammetric DSM. Gaussian centers are sampled from DSM pixels with area-weighted probability, with denser sampling near high local surface variation; normals are initialized from DSM gradients and disk scales aligned to the surface (Kim et al., 25 Jun 2026). Because satellite sensors use RPC camera models, SatSplatDiff fits an affine camera $F = [W \mid b]$ per image for efficient rendering and optimization (Kim et al., 25 Jun 2026). This affine approximation is then reused in the multi-scale refinement stage, where cameras are sampled over elevation $\theta$, azimuth $\mu_i \in \mathbb{R}^3$0, zoom $\mu_i \in \mathbb{R}^3$1, and target translation $\mu_i \in \mathbb{R}^3$2.

The early geometric stage adds two regularizing priors. First, monocular depth supervision is applied for roughly the first 3,000 iterations using a scale-invariant Pearson correlation loss between rendered depth and the monocular prior,

$\mu_i \in \mathbb{R}^3$3

which stabilizes early optimization without imposing absolute depth (Kim et al., 25 Jun 2026). Second, multi-scale geometric refinement renders the scene from zoomed, rotated, and translated affine cameras to expose façades and encourage solidity. The refinement loss combines distortion, normal consistency, and opacity entropy: $\mu_i \in \mathbb{R}^3$4 The distortion term collapses splats in depth, the normal term aligns primitive normals with depth-gradient normals, and the entropy term pushes opacities toward a solid surface representation (Kim et al., 25 Jun 2026).

Adaptive densification is also modified. SatSplatDiff clones or splits Gaussians based on scale gradients and revises opacity after splitting using

$\mu_i \in \mathbb{R}^3$5

then prunes splats with $\mu_i \in \mathbb{R}^3$6 (Kim et al., 25 Jun 2026). This is intended to avoid accumulation and overgrowth during refinement. The net effect is a geometry stage that is considerably more structured than standard appearance-only optimization.

A defining component is 2DGS-based shadow casting. The sun is modeled as an inverse camera derived from the satellite camera and solar direction, enabling differentiable shadow visibility. The visibility per pixel is

$\mu_i \in \mathbb{R}^3$7

and final image formation is

$\mu_i \in \mathbb{R}^3$8

A shadow entropy term,

$\mu_i \in \mathbb{R}^3$9

keeps shadows near-binary and discourages texture from being baked into visibility (Kim et al., 25 Jun 2026).

4. Shadow-guided generative refinement

Once geometry is regularized, SatSplatDiff introduces diffusion-based appearance enhancement. The generative stage samples diverse novel affine views and sun directions, renders albedo, casts geometry-driven shadows, and feeds the resulting shadow-cast renders to a pretrained diffusion model, FLUX.2 [klein] 4B, using geometry-preserving prompts emphasizing strict rectilinear lines, crisp façades, preserved shadows, maintained exposure, and sensor consistency (Kim et al., 25 Jun 2026). These prompts are not generic stylistic text conditioning; they are part of a geometry-preserving design intended to suppress structural hallucination.

The refined pseudo-views are not used in isolation. SatSplatDiff mixes diffusion-refined pseudo-views with original satellite images and supervises the Gaussian model with the standard image loss

$\Sigma_i \in \mathbb{R}^{3 \times 3}$0

together with geometric regularization terms inherited from the refinement stage (Kim et al., 25 Jun 2026). In the geometric stage, the total objective is

$\Sigma_i \in \mathbb{R}^{3 \times 3}$1

while the generative stage deactivates $\Sigma_i \in \mathbb{R}^{3 \times 3}$2 and optimizes $\Sigma_i \in \mathbb{R}^{3 \times 3}$3 on mixed real and pseudo views plus the regularizers (Kim et al., 25 Jun 2026).

The paper’s central claim is that shadow guidance prevents the geometry drift typical of view-independent generative refinement. Diffusion refines only the albedo conditioned by shadow-cast renders; shadow boundaries are geometry-driven and consistent across views; and gradients through $\Sigma_i \in \mathbb{R}^{3 \times 3}$4 remain tied to Gaussian positions. This makes it difficult for purely photometric refinements to alter shadow structure unless the underlying geometry changes as well (Kim et al., 25 Jun 2026). A plausible implication is that the method uses shadow maps as a physically structured bridge between a generative prior and a geometry optimizer, rather than treating diffusion outputs as unconstrained pseudo-ground truth.

The refinement is iterative: re-render, re-shadow, re-refine, and update geometry and appearance (Kim et al., 25 Jun 2026). This loop is the distinctive element of SatSplatDiff as a satellite method. It does not merely append diffusion to Gaussian Splatting; it constrains diffusion with solar geometry and re-anchors the refinement with real observations.

5. Training protocol, datasets, and empirical performance

The implementation is explicitly staged. The geometric stage runs for 12,000 iterations, with monocular depth active for the first roughly 3,000 iterations. The generative stage then performs 10,000 iterations per cycle for 5 cycles, using $\Sigma_i \in \mathbb{R}^{3 \times 3}$5 refined views at $\Sigma_i \in \mathbb{R}^{3 \times 3}$6 (Kim et al., 25 Jun 2026). Reported loss weights are $\Sigma_i \in \mathbb{R}^{3 \times 3}$7, $\Sigma_i \in \mathbb{R}^{3 \times 3}$8, $\Sigma_i \in \mathbb{R}^{3 \times 3}$9, $c_i$0, $c_i$1, and $c_i$2 (Kim et al., 25 Jun 2026). Learning rates are staged as well: $c_i$3 for Gaussian means in the geometric stage and $c_i$4 in the generative stage, $c_i$5 for opacities, $c_i$6 for rotations and scales, $c_i$7 for colors, $c_i$8 for color correction, and $c_i$9 for ambient illumination $\alpha_i$0 (Kim et al., 25 Jun 2026).

The paper evaluates on DFC2019 and IARPA2016. DFC2019 includes Jacksonville and Omaha with $\alpha_i$1 panchromatic imagery at 35 cm/pixel and LiDAR DSM ground truth over $\alpha_i$2 tiles at 0.5 m/pixel. IARPA2016 contains roughly 50 commercial satellite images over roughly $\alpha_i$3, again with LiDAR-derived DSM ground truth (Kim et al., 25 Jun 2026). Metrics span geometry and appearance: registered geometric MAE, PSNR, SSIM, CW-SSIM, LPIPS, FID-CLIP, and CMMD (Kim et al., 25 Jun 2026).

Quantitatively, SatSplatDiff reports mean $\alpha_i$4 down to $\alpha_i$5. Per dataset, JAX reaches $\alpha_i$6, which is stated as $\alpha_i$7 versus EOGS at $\alpha_i$8; OMA reaches $\alpha_i$9; and IARPA reaches $D_{\text{render}}(u) = \sum_{i=1}^{N} w_i(u) z_i.$0 (Kim et al., 25 Jun 2026). On visual distribution metrics, FID-CLIP is reported as 19.50 for JAX, 19.06 for OMA, and 29.50 for IARPA, described as 28–45% lower than second-best baselines (Kim et al., 25 Jun 2026). The method also reports improved PSNR, CW-SSIM, and LPIPS relative to baselines, up to $D_{\text{render}}(u) = \sum_{i=1}^{N} w_i(u) z_i.$1 effective resolution enhancement, façade recovery, sharp boundaries, clean roofs, and seamless cross-tile mosaics (Kim et al., 25 Jun 2026).

Ablation results are central to the argument. Multi-scale refinement improves FID-CLIP from 19.56 to 19.50, CW-SSIM from 0.410 to 0.414, reduces $D_{\text{render}}(u) = \sum_{i=1}^{N} w_i(u) z_i.$2 from 1.27 to 1.25, and increases average opacity from 0.97 to 0.99 (Kim et al., 25 Jun 2026). Generative refinement improves FID-CLIP from 48.34 to 19.50 while preserving geometry, with $D_{\text{render}}(u) = \sum_{i=1}^{N} w_i(u) z_i.$3 changing from 1.28 to 1.25; by contrast, Skyfall-GS is reported to degrade geometry from 1.85 to 1.93 under enhancement (Kim et al., 25 Jun 2026). Shadow guidance is also ablated, with the best geometry reported for the shadow-guided configuration and FID-CLIP 19.50 under random sun sampling (Kim et al., 25 Jun 2026).

From a systems standpoint, the method runs on a single NVIDIA RTX 6000 ADA with about 23 GB GPU memory. The geometric stage takes roughly 42–49 minutes per tile depending on multi-scale refinement, and reconstructions contain approximately 2.43–2.46 million splats (Kim et al., 25 Jun 2026). Cross-tile mosaics are merged via seam bisectors, with shadow-guided refinement and per-image radiometric correction contributing to seamlessness (Kim et al., 25 Jun 2026).

6. Relation to adjacent work, alternate usage, and limitations

Within satellite reconstruction, SatSplatDiff is explicitly framed as an extension of SatSplat. The retained foundations are 2DGS oriented disks, differentiable shadow casting with affine camera fitting, and photogrammetric DSM initialization; the new elements are monocular depth supervision, multi-scale geometric refinement with opacity entropy, revised densification opacity, and shadow-guided generative refinement with solar sampling and pseudo-dataset mixing (Kim et al., 25 Jun 2026). Relative to EO-GS and EOGS++, the method is described as preserving or surpassing DSM accuracy while adding façade detail; relative to Skyfall-GS, its defining claim is that it improves texture without the geometry drift caused by view-independent hallucination (Kim et al., 25 Jun 2026).

The broader Gaussian-splat diffusion literature uses related ideas but in materially different settings. The single-image method summarized as SatSplatDiff in the supplied material reconstructs complete 3D scenes from one posed RGB image using a Variational AutoReconstructor and a latent diffusion model over Splatter Images, with diverse sampling of occluded and out-of-frustum completions (Liao et al., 29 Aug 2025). Splat4D extends diffusion-enhanced Gaussian Splatting to temporally and spatially consistent 4D generation from monocular video, with uncertainty masks and video diffusion refinement (Yin et al., 11 Aug 2025). SplatDiff addresses single-view novel view synthesis using pixel-splatting guidance and a video diffusion backbone (Zhang et al., 18 Feb 2025). These are related by their use of Gaussian or splatting representations plus diffusion, but they solve different problems and employ different supervisory structures.

The satellite method also has explicit limitations. It is sensitive to DSM quality: incomplete or misaligned initialization can produce incorrect shadows that reinforce bad geometry (Kim et al., 25 Jun 2026). Sparse-view regimes with fewer than roughly 12 images were observed to destabilize geometry, and very oblique façades remain weakly constrained (Kim et al., 25 Jun 2026). Extreme shadows, haze, specular or high-reflectance roofs, and thin structures such as roller coasters remain difficult; strong smoothness and solidity can omit very thin isolated elements (Kim et al., 25 Jun 2026). The diffusion prior also tends to "beautify," which the paper mitigates through prompts, shadow conditioning, and mixing original images (Kim et al., 25 Jun 2026).

Taken together, SatSplatDiff is best understood as a geometry-preserving generative refinement strategy for satellite Gaussian Splatting in which shadow casting is not ancillary but structural. It supplies the mechanism that keeps diffusion-enhanced appearance compatible with a physically grounded surface model. In the wider diffusion-and-splats literature, the same label may refer more loosely to other generative Gaussian-splat pipelines, but the satellite formulation is the one that most fully defines the term as a method name in the supplied corpus (Kim et al., 25 Jun 2026).