DeformSplat: Deformable Gaussian Splatting

• DeformSplat is a framework for deformable Gaussian splatting that uses affine transformations to modify canonical 3D models for new viewpoints or time sequences.
• It employs rigidity-aware loss functions and Gaussian-to-Pixel matching to accurately reconstruct deformations from single RGB images, demonstrating strong performance on datasets like Diva360 and DFA.
• It extends to dynamic scenes and view-dependent editing by integrating per-Gaussian embeddings and cage-based deformations for realistic, interactive 3D transformations.

Searching arXiv for the cited DeformSplat-related papers and adjacent work. DeformSplat denotes a class of deformable splatting formulations in which a canonical set of splats is transformed to represent new geometry, viewpoints, or time, and it also names a specific rigidity-aware framework for reconstructing deformation of a pre-reconstructed 3D Gaussian scene from only a single RGB image (Kim et al., 26 Sep 2025). In the single-image setting, the canonical scene is a 3D Gaussian field $\mathcal{G}=\{\mu_i,q_i,s_i,\alpha_i,sh_i\}$, the target is an unposed image $\mathcal{I}_{\text{target}}$, and the deformed output is $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$, with deformation applied to Gaussian centers and rotations while appearance parameters remain fixed (Kim et al., 26 Sep 2025). In adjacent literature, the same conceptual space includes view-dependent deformation fields for 2D-guided editing (Mqirmi et al., 7 Apr 2025), canonical-field dynamic Gaussian models (Bae et al., 2024, Lu et al., 2024, Jiao et al., 21 Mar 2026, Deng et al., 11 Jun 2025), mesh- and cage-guided non-rigid deformation (Xie et al., 2024, B, 9 Jul 2025, Fehrentz et al., 23 Sep 2025), proxy-free Laplacian deformation (Kim et al., 24 Nov 2025), and a general theory in which splats are affine deformations of a mother density and Gaussian Splatting is a special case (Daniels et al., 18 Nov 2025).

1. Formal notion of deformable splats

In the most general formulation, a splat is a parametrically transformed bump function obtained from a fixed mother density $\rho \in P_{ac}(\mathbb{R}^d)$ by an affine map. For parameters $A \in \mathbb{R}^{d\times d}$ and $b \in \mathbb{R}^d$, the transformed density is

$$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$

The location parameter $b$ controls the center, while $A$ controls scale and orientation, which is where anisotropy and deformation reside (Daniels et al., 18 Nov 2025).

The associated function class is defined through a mixing measure $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$, with model

$\mathcal{I}_{\text{target}}$0

For a finite $\mathcal{I}_{\text{target}}$1-splat measure this becomes a finite mixture of anisotropically deformed bumps weighted by output vectors $\mathcal{I}_{\text{target}}$2, with parameters $\mathcal{I}_{\text{target}}$3 encoding local output values, $\mathcal{I}_{\text{target}}$4 encoding positions, and $\mathcal{I}_{\text{target}}$5 encoding local scales and directions (Daniels et al., 18 Nov 2025). This provides the cleanest mathematical reading of “deformable splats”: splats are explicit geometric entities whose shape and placement are optimized rather than fixed.

This formalism also subsumes Gaussian Splatting. If the mother splat is the standard Gaussian $\mathcal{I}_{\text{target}}$6, then

$\mathcal{I}_{\text{target}}$7

so Gaussian splats appear as a special case of splat regression (Daniels et al., 18 Nov 2025). The paper further states that this viewpoint “disambiguates the inverse problem, the model, and the optimization algorithm,” separating the forward operator, the splat representation, and the fitting rule (Daniels et al., 18 Nov 2025). A plausible implication is that the name DeformSplat is best understood not as a single algorithmic recipe, but as a design space built around affine-deformable splat primitives.

2. Rigidity-aware DeformSplat from a single image

The paper explicitly titled “Rigidity-Aware 3D Gaussian Deformation from a Single Image” introduces DeformSplat as a framework for deforming a canonical 3DGS model using one target RGB image of a new configuration (Kim et al., 26 Sep 2025). The method assumes a pre-reconstructed canonical Gaussian scene and an unknown target-camera pose. Only Gaussian centers and rotations are optimized; scales, opacity, and spherical-harmonic appearance remain fixed to avoid color overfitting (Kim et al., 26 Sep 2025).

Its first core component is Gaussian-to-Pixel Matching. The canonical Gaussians are rendered from all known reconstruction cameras, each rendered view is matched to the target image with RoMA, and the view with the highest spatial overlap is selected. Dense 2D correspondences are then lifted to Gaussian-to-Pixel pairs $\mathcal{I}_{\text{target}}$8, where $\mathcal{I}_{\text{target}}$9 is a visible Gaussian center and $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$0 is the matched target pixel (Kim et al., 26 Sep 2025). This yields the deformation loss

$\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$1

which provides explicit 3D-to-2D geometric supervision rather than relying only on image reconstruction (Kim et al., 26 Sep 2025).

The second core component is Rigid Part Segmentation, consisting of initialization and refinement. Initialization combines PnP-RANSAC with a region-growing strategy to form spatially coherent rigid groups from Gaussian-to-Pixel correspondences. Refinement uses a rigidity score

$\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$2

and adds or removes Gaussians from rigid groups according to thresholds $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$3 and $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$4 (Kim et al., 26 Sep 2025). This explicitly separates regions that should preserve internal structure from regions where non-rigid deformation is admissible.

The deformation model itself is anchor-based. Sparse anchors are obtained by voxelizing space, and each anchor carries a rotation and translation. Gaussian positions and rotations are interpolated from neighboring anchor transforms: $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$5 Optimization minimizes the total objective

$\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$6

where $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$7 preserves relative geometry inside rigid groups and $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$8 regularizes local deformation between anchors (Kim et al., 26 Sep 2025). The same framework naturally supports frame interpolation and interactive manipulation via target correspondences supplied by either additional images or user interaction (Kim et al., 26 Sep 2025).

Quantitatively, the reported results on Diva360 are PSNR $\mathcal{G}'=\{\mu_i',q_i',s_i,\alpha_i,sh_i\}$9, SSIM $\rho \in P_{ac}(\mathbb{R}^d)$0, and LPIPS $\rho \in P_{ac}(\mathbb{R}^d)$1, and on DFA are PSNR $\rho \in P_{ac}(\mathbb{R}^d)$2, SSIM $\rho \in P_{ac}(\mathbb{R}^d)$3, and LPIPS $\rho \in P_{ac}(\mathbb{R}^d)$4 (Kim et al., 26 Sep 2025). The paper reports that removing deformation loss and group loss reduces Diva360 PSNR to $\rho \in P_{ac}(\mathbb{R}^d)$5, while removing group loss only yields $\rho \in P_{ac}(\mathbb{R}^d)$6, indicating that rigidity-aware geometric supervision is central rather than auxiliary (Kim et al., 26 Sep 2025).

3. View-conditioned and sketch-driven deformation

A distinct branch of DeformSplat-like work treats deformation as a function of viewpoint rather than time. “View-Dependent Deformation Fields for 2D Editing of 3D Models” defines a view-dependent deformation field

$\rho \in P_{ac}(\mathbb{R}^d)$7

with the congruence condition

$\rho \in P_{ac}(\mathbb{R}^d)$8

so that the deformed 3D object matches a user-authored 2D deformation $\rho \in P_{ac}(\mathbb{R}^d)$9 at key view $A \in \mathbb{R}^{d\times d}$0 (Mqirmi et al., 7 Apr 2025). Each 2D warp is lifted to 3D by preserving depth in camera coordinates, and multiple deformations are blended compositionally through recursive view-dependent interpolation

$A \in \mathbb{R}^{d\times d}$1

where $A \in \mathbb{R}^{d\times d}$2 are localized basis functions on the viewing sphere (Mqirmi et al., 7 Apr 2025).

For 3D Gaussian splats, the method uses a first-order Taylor approximation of the deformation around each Gaussian center $A \in \mathbb{R}^{d\times d}$3,

$A \in \mathbb{R}^{d\times d}$4

which preserves Gaussian form under deformation by updating

$A \in \mathbb{R}^{d\times d}$5

This yields view-dependent deformation of both centers and covariances while remaining compatible with standard 3DGS rendering (Mqirmi et al., 7 Apr 2025). The same paper reports interactive performance of approximately $A \in \mathbb{R}^{d\times d}$6 FPS on an NVIDIA RTX 4090 for models with $A \in \mathbb{R}^{d\times d}$7 Gaussians, with BBW preprocessing around $A \in \mathbb{R}^{d\times d}$8 ms and triangulation around $A \in \mathbb{R}^{d\times d}$9 ms (Mqirmi et al., 7 Apr 2025).

A second editing-oriented line is “Sketch-guided Cage-based 3D Gaussian Splatting Deformation,” which couples cage-based deformation with a variant of Neural Jacobian Fields (Xie et al., 2024). A deformation cage $b \in \mathbb{R}^d$0 encloses the splat set, the cage interpolation map $b \in \mathbb{R}^d$1 moves Gaussian means,

$b \in \mathbb{R}^d$2

and the covariance update is given by

$b \in \mathbb{R}^d$3

The cage is controlled through per-face Jacobians decomposed into rotations and symmetric stretches, and optimization combines a silhouette term with 3D-aware SDS: $b \in \mathbb{R}^d$4 This formulation turns silhouette sketches into geometrically consistent deformation of 3D Gaussian models, and the paper presents animation as a direct extension obtained by interpolating keyframe cages over time (Xie et al., 2024).

4. Dynamic-scene deformation architectures

In dynamic view synthesis, DeformSplat usually refers to a canonical Gaussian field plus a learned deformation model. “Per-Gaussian Embedding-Based Deformation for Deformable 3D Gaussian Splatting” argues that coordinate-based deformation fields are mismatched to Gaussian splatting and replaces them with a deformation function of per-Gaussian embeddings $b \in \mathbb{R}^d$5 and temporal embeddings $b \in \mathbb{R}^d$6: $b \in \mathbb{R}^d$7 It further decomposes motion into coarse and fine branches,

$b \in \mathbb{R}^d$8

to separate slow, large motion from fast, localized motion (Bae et al., 2024). The reported averages are PSNR $b \in \mathbb{R}^d$9, SSIM $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$0, and LPIPS $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$1 on Neural 3D Video; PSNR $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$2, SSIM $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$3, and LPIPS $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$4 on Technicolor; and PSNR $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$5, SSIM $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$6, and LPIPS $$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$7 on HyperNeRF (Bae et al., 2024).

“3D Geometry-aware Deformable Gaussian Splatting for Dynamic View Synthesis” instead conditions deformation on explicit 3D geometry features extracted from canonical Gaussians by a sparse 3D U-Net (Lu et al., 2024). Time-dependent position, scale, and rotation are predicted as

$$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$8

with updates

$$\rho_{A,b} \coloneqq (A(\cdot)+b)_\#\rho, \qquad \rho_{A,b}(x)=\rho(A^{-1}(x-b))\,|\det A^{-1}|.$$9

A motion penalty $b$0 is added to the photometric objective (Lu et al., 2024). On D-NeRF, the method reports PSNR $b$1, SSIM $b$2, and LPIPS $b$3 for Hell Warrior, and PSNR $b$4, SSIM $b$5, and LPIPS $b$6 for Mutant (Lu et al., 2024).

Recent work emphasizes speed and robustness. FRoG keeps canonical Gaussians $b$7, uses per-Gaussian embeddings $b$8, and fuses coarse and fine temporal embeddings by Hadamard product,

$b$9

so that one MLP pass predicts all attribute deltas (Jiao et al., 21 Mar 2026). It augments this with depth- and error-guided canonical sampling and opacity modulation

$A$0

to mitigate local optima in dim scenes (Jiao et al., 21 Mar 2026). DynaSplat, by contrast, explicitly separates static and dynamic Gaussians using deformation variance and 2D motion flow consistency, then decomposes motion into coarse neighbor-averaged dynamics and fine residuals, while also using physically-based opacity and temporal importance filtering (Deng et al., 11 Jun 2025). This suggests that “dynamic DeformSplat” has evolved from a single deformation field into a family of structured motion models with explicit partitioning, hierarchy, and visibility reasoning.

5. Physics, anatomy, and transient decomposition

Another interpretation of DeformSplat replaces purely kinematic deformation with domain-specific constraints. Physics-Informed Deformable Gaussian Splatting treats each Gaussian as a Lagrangian material point and couples a deformation network with a time-evolving material field predicting velocity $A$1 and stress $A$2 (Hong et al., 9 Nov 2025). The governing residual is the Cauchy momentum residual

$A$3

with training term

$A$4

The method adds Lagrangian particle flow matching against camera-compensated optical flow,

$A$5

to accelerate convergence and improve generalization (Hong et al., 9 Nov 2025). The stated goal is a unified constitutive framework for time-evolving material fields rather than unconstrained deformation.

BridgeSplat imports anatomical priors by rigging Gaussians to a CT-derived mesh for deformable surgical navigation (Fehrentz et al., 23 Sep 2025). Each Gaussian mean is parametrized barycentrically on a parent mesh triangle,

$A$6

and mesh vertices are moved by a sparse anchor deformation field $A$7 (Fehrentz et al., 23 Sep 2025). Photometric supervision is combined with ARAP regularization on the mesh, and deformations are propagated back to the preoperative CT. On synthetic liver simulations, the reported mean Euclidean distances are $A$8 mm for SimIn, $A$9 mm for SimDown, $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$0 mm for SimLeft, $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$1 mm for SimCircular, and $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$2 mm for SimUp, with maximum Euclidean distance below $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$3 mm in all cases (Fehrentz et al., 23 Sep 2025).

ForestSplats uses deformation in a different sense: a deformable transient field explains per-view transient content in unconstrained image collections (Park et al., 8 Mar 2025). The rendered image is decomposed as

$$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$4

where $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$5 is the static field, $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$6 is the transient field, and $$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$7 is a learned superpixel-aware mask (Park et al., 8 Mar 2025). The transient field is driven by per-view embeddings and deformation offsets,

$$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$8

and is combined with uncertainty-aware densification to avoid placing static Gaussians inside transient regions (Park et al., 8 Mar 2025). This broadens DeformSplat from surface motion to view-specific scene decomposition.

6. Surface priors, proxies, limitations, and outlook

Surface structure is a central fault line in the DeformSplat literature. One response is to add explicit topology. “Enhancing non-Rigid 3D Model Deformations Using Mesh-based Gaussian Splatting” anchors Gaussians to explicit mesh surfaces reconstructed from a 3DGS scene, uses XPBD for non-rigid deformation, and updates Gaussian covariance under the deformation Jacobian as

$$\mu \in P(\mathbb{R}^p \times {}_\rho(\mathbb{R}^d))$$9

The paper positions the mesh as a carrier of topological, geometric, and physical priors, allowing moving, scaling, rotating, bending, and stretching of components while maintaining real-time rendering (B, 9 Jul 2025). A closely related perspective appears in sketch-guided cage deformation, where the cage is not itself the visible surface but a low-dimensional control domain for Gaussian motion (Xie et al., 2024).

The opposite response is proxy-free surface inference. SpLap introduces a surface-aware splat graph in which neighboring splats are defined by intersection of occupancy regions rather than by center distance (Kim et al., 24 Nov 2025). For splat $\mathcal{I}_{\text{target}}$00, the occupancy region is

$\mathcal{I}_{\text{target}}$01

and graph edges are created if the normal-wise offset $\mathcal{I}_{\text{target}}$02 between occupancy regions satisfies $\mathcal{I}_{\text{target}}$03 (Kim et al., 24 Nov 2025). Classical ARAP and BBW are then applied directly on the splat graph, and kernel adaptation is performed by transporting a maximum-area inscribed triangle through the deformation and reconstructing the Gaussian via the Steiner circumellipse (Kim et al., 24 Nov 2025). The paper reports superior performance over both proxy-based and proxy-free baselines on $\mathcal{I}_{\text{target}}$04 objects from ShapeNet, Objaverse, Sketchfab, and NeRF-Synthetic (Kim et al., 24 Nov 2025).

Several recurrent limitations emerge across these formulations. Single-image DeformSplat depends strongly on matching quality and assumes meaningful rigid components; highly non-rigid objects and appearance change remain difficult (Kim et al., 26 Sep 2025). View-dependent editing can produce artifacts for large Gaussians because affine approximation is local (Mqirmi et al., 7 Apr 2025). Physics-informed approaches remain optimization-heavy and use simplified constitutive assumptions (Hong et al., 9 Nov 2025). Mesh-guided methods inherit the constraints of fixed topology, making tearing or topological change poorly supported (B, 9 Jul 2025). Proxy-free Laplacian methods rely on well-aligned surface splats and do not themselves repair poor reconstruction (Kim et al., 24 Nov 2025). A plausible synthesis is that DeformSplat is not converging toward a single canonical architecture; instead, it is stratifying into multiple regimes distinguished by the source of deformation evidence—single-image correspondences, view-conditioned edits, temporal motion, physics, anatomy, or surface graph structure—and by the strength of the prior used to keep Gaussian deformation geometrically coherent.