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Make It Flow: Animating Water in 3D Gaussian Splatting Scenes
Kjell Keune, Florian Hahlbohm, Jannis Möller, Susana Castillo, Martin Eisemann, Marcus Magnor
TL;DR
Static 3DGS scenes often leave flowing water frozen, and casual capture makes dynamic reconstruction difficult. This method lifts 2D flow into a 3D motion field and animates Gaussians in looping sequences. On seven casually captured scenes, it produces more realistic, temporally coherent renderings than prior work while remaining computationally efficient.
Problem
Static 3DGS scenes often fail to capture dynamic phenomena such as water, while casual capture limits the dense synchronized views needed by dynamic reconstruction methods.
Source: §1 · pp. 1–2Method
Results
The method produces more realistic and temporally coherent novel-view renderings than prior work while remaining computationally efficient.
Source: §1 · p. 2Takeaways & Limitations
The approach adds plausible looping water motion to static scenes while preserving real-time rendering and free-viewpoint navigation.
Source: §6 · p. 9Motion quality depends on the 3DGS reconstruction; reflective or ambiguous water may lack enough Gaussians, and motion is largely confined to the visible surface.
Source: §5 · p. 9
Abstract
from arXiv · showhide
Explicit 3D scene representations such as 3D Gaussian Splatting (3DGS) have recently enabled high-quality, real-time novel view synthesis. However, these methods assume static scenes, limiting realism in the presence of dynamic phenomena ubiquitous in real-world environments. While coherent motion (e.g., humans or vehicles) can be captured and reconstructed, high-frequency effects such as flowing water remain intractable under casual capture conditions, where dense multi-view, high-speed acquisition is not feasible. We present a method to animate water in static 3DGS scenes, enabling visually plausible motion without requiring dynamic capture or physical simulation. Our approach estimates 2D optical flow from reference images or model renderings and lifts it into a consistent 3D Eulerian motion field. We propose a cinemagraph-inspired algorithm that applies this motion field to deform Gaussian primitives, producing temporally seamless looping animations. The resulting representation retains real-time rendering performance, significantly enhances perceptual realism, and preserves free-viewpoint navigation within the scene. We evaluate our method on a newly captured dataset of in-the-wild waterfall scenes and demonstrate clear improvements over prior work in dynamic Gaussian splatting and 3D cinemagraph generation in visual quality and computational efficiency.
1. Introduction
Flowing water remains difficult to represent in static 3DGS scenes, especially under casual capture; this work adds plausible, looping water motion and reports more realistic, temporally coherent renderings at low computational cost.
1. Introduction
- Static reconstructions often leave water frozen, while dynamic methods focus on foreground objects and commonly require synchronized multi-view capture or costly physical simulation.The paper instead targets visually plausible motion rather than physically accurate simulation.Source: §1 · pp. 1–2
- Earlier 3D cinemagraph methods either render slowly with limited free-viewpoint capability or lack enough structure to recover realistic fluid motion [LCS∗23, LCW∗24].These limitations motivate the paper's more efficient approach to plausible water animation in static 3DGS scenes.Source: §1 · p. 2
- The method estimates per-view fluid flow and lifts it into a 3D Eulerian motion field, then deforms Gaussian primitives with a 3D adaptation of symmetric warping.The adaptation uses volume-aware covariance propagation, density-preserving opacity blending, and randomized temporal offsets.Source: §1 · p. 2
- The method produces more realistic and temporally coherent novel-view renderings than prior work while remaining computationally efficient.The evaluation uses a newly captured dataset of seven casually captured scenes with fluid phenomena such as waterfalls.Source: §1 · p. 2
- The approach animates fluid regions in static 3DGS scenes without dynamic capture, retraining, or simulation, and supports real-time rendering and interactive exploration.The authors also introduce a dataset of seven casual scenes with fluid motion.Source: §1 · p. 2
2. Related Work
Prior work spans static and dynamic scene representations, 2D cinemagraph synthesis, and attempts to extend looping motion to 3D. The paper positions its approach as an efficient way to add controllable fluid motion to static 3DGS scenes.
2.1. Novel View Synthesis
- Dynamic scene methods can reconstruct structured motion, but controlled capture or strong priors limit casual use, and subtle continuous water motion is a poor fit for their assumptions.3DGS provides an explicit scene representation optimized for real-time rasterization.Source: §2.1 · p. 2
2.2. Cinemagraphs and Motion Synthesis
- Cinemagraphs support perceptually convincing looping fluid motion, while learning-based synthesis and repeated inference can limit real-time use [SSSE00, LJH13, LFH15, TPSK11, HHB18, GXG18, EKK19, LIM∗26].Static or quasi-static motion fields offer efficient looping and inform the paper's motion-generation framework [HCSS21, MK22, HHV∗21].Source: §2.2 · p. 2
- 3D cinemagraph approaches can lack viewpoint flexibility or reconstruction quality, while Gaussian or neural methods may rely on similarity, specialized priors, or costly pipelines that impede coherent directional fluid motion [LCS∗23, MLLS23, LCW∗24, JMG∗25].Physics-based fluid methods can be costly, require per-scene setup, or alter scene appearance; oscillatory motion models do not readily generalize to fluids [FFS∗25, SHK∗24, LGB∗26, THM∗26].Source: §2.2 · pp. 2–3
- In contrast to dynamic reconstruction, learned 3D cinemagraph approaches, and physics-based simulation, the paper augments static 3DGS scenes with motion derived from 2D flow priors, enabling efficient, controllable fluid animation without reconstructing a fully dynamic scene.Source: §2.2 · p. 3
3. Method
Given a static 3DGS scene and input views, the pipeline estimates fluid flow, lifts it into a 3D motion field, and uses that field to animate dynamic Gaussians in looping sequences.
3.1. Optical Flow Estimation
- A learned flow-refinement network uses RGB images, segmentation masks, dense flow maps, and user-defined hints to estimate fluid motion in each view.The hints are defined in 3D for cross-view consistency, while masks guide flow synthesis and restrict motion to fluid regions.Source: §3.1 · p. 4
3.2. 3D Motion Field
- Depth-based multi-view reprojection combines the per-view optical flows to estimate a coherent 3D motion vector at each scene point.The method linearizes the projection and solves the resulting system with iterative Gauss–Newton optimization.Source: §3.2 · p. 4
3.2.1. Voxel Grid Fusion
- Per-voxel flow estimates are accumulated across views, solved as 3×3 systems, and stored in a sparse grid after one-time fusion.Views contribute once per voxel; GPU-accelerated linear algebra solves the systems in parallel.Source: §3.2.1 · pp. 4–5
3.2.2. Refinement
- Static-region hits reduce motion in likely static voxels, while voxels with too few view hits are assigned zero motion.The view-hit threshold addresses ill-posed estimates when observations are limited or viewing directions are mostly collinear.Source: §3.2.2 · p. 5
3.3. Gaussian Animation and Rendering
- Dynamic Gaussians are selected by querying the motion field at their means, while Gaussians in static regions remain unchanged.The scene is split into static and dynamic sets using whether the queried motion magnitude is nonzero.Source: §3.3 · p. 5
3.3.1. Transforming Gaussians
- An Unscented Transform propagates each dynamic Gaussian’s mean and covariance by displacing seven sigma points with queried motion.Euler integration iterates the transform, and a regulation factor controls motion extent when the field lacks physically meaningful velocities.Source: §3.3.1 · p. 5
3.3.2. Symmetric Animation
- Forward and backward transforms use M and −M; opacity cross-fading at the shared original state supports seamless loops, while per-Gaussian offsets reduce repeated patterns.The negated field is an approximation rather than a general inverse; paired instances share the same offset to preserve symmetric transformation.Source: §3.3.2 · pp. 5–6
3.3.3. Rendering
- Virtual Gaussian instances share animation-independent buffers, and neighboring keyframes are linearly interpolated for smoother rendering.The implementation uses a CUDA renderer; covariance interpolation is not exact for rotation but is described as a visually smooth, efficient alternative.Source: §3.3.3 · p. 6
4. Evaluation
Evaluation uses seven casually captured fluid scenes, compares novel-view animations against dynamic Gaussian and 3D cinemagraph baselines, and assesses motion quality qualitatively and efficiency quantitatively. All experiments use an RTX 4090; motion quality is judged qualitatively because casually captured scenes lack ground-truth motion and suitable no-reference fluid-motion metrics (p20).
4.1. Dataset
- The dataset contains seven casually captured scenes with waterfalls of varied scales and shapes, a cascading creek, and a weir.Scenes were captured with DSLR photographs or drone video clips; the release also includes motion hints, motion fields, and dynamic-Gaussian masks.Source: §4.1 · p. 6
4.2. Baselines
- Comparisons use novel viewpoints and four-second, 240-frame loops, with 3D-Cinemagraphy limited to 60 frames.The baselines are 4DGS, LoopGaussian, and 3D-Cinemagraphy; LoopGaussian’s motion field and animation are integrated into the authors’ framework for comparison.Source: §4.2 · p. 6
4.3. Qualitative Comparisons
- Our method produces more plausible, temporally coherent novel-view water motion than 3D-Cinemagraphy, 4DGS, and LoopGaussian.3D-Cinemagraphy degrades as viewpoints move from its reference pose, 4DGS struggles with high-frequency water dynamics, and LoopGaussian’s motion lacks coherent fluid flow.Source: §4.3 · pp. 6–7, Figure 3 · p. 7
4.4. Quantitative Comparisons
- All Gaussian methods exceed 300 FPS; 4DGS uses 2.7 GiB average VRAM versus our 3.8 GiB, while LoopGaussian reaches 8.7 GiB on “Frogfall” versus our 5.5 GiB.Motion-field preprocessing averages approximately one minute for our method versus around six minutes for LoopGaussian, reaching roughly thirteen minutes on “Waterfall”; our fused sparse field averages 2 MB.Source: Table 2 · p. 7, §4.4 · pp. 7–8, Table 3 · p. 8
4.5. Ablation Study
- Opacity blending and random state offsets prevent visible loop cuts and recurring patterns; motion refinements suppress unwanted or incoherent movement.A single directional hint suffices in some scenes, but waterfall-to-river transitions require additional hints.Source: §4.5 · p. 8
- Static-region refinement and view-hit thresholding reduce unwanted motion and incoherent flow caused by reprojection.Thresholding also reduces voxels in empty regions to better fit the dynamic Gaussian region.Source: §4.5 · p. 8
5. Discussion, Limitations, and Future Work
The method efficiently animates fluid in static 3DGS scenes and can also handle lava. Its motion-field quality depends on the underlying reconstruction, and future work could add dynamic updates for responsive behavior.
5. Discussion, Limitations, and Future Work
- The method integrates plausible fluid animation into static 3DGS scenes without requiring a fully dynamic reconstruction and also generalizes to lava.The motion field is precomputed once and stored compactly; flow inputs may be training images, user-defined renderings, or both for targeted refinement.Source: §5 · pp. 8–9
- Motion quality depends on the 3DGS reconstruction: depth errors, artifacts, or poorly reconstructed reflective or ambiguous surfaces can cause inaccurate motion and visible artifacts.The method cannot recover fluid detail absent from the reconstruction, and motion is largely confined to the visible water surface.Source: §5 · p. 9
- Future work could dynamically update the motion field so fluids can respond to user interaction or external scene events while maintaining real-time performance.The stated direction is interactive or physically responsive fluid behavior.Source: §5 · p. 9
6. Conclusion
The paper concludes that cinemagraph-inspired motion synthesis can animate water in static 3DGS scenes while retaining real-time rendering and free-viewpoint navigation. Its experiments report more plausible water motion than prior methods at low computational cost.
6. Conclusion
- The method lifts 2D fluid motion into a coherent 3D Eulerian field and deforms Gaussian primitives to create seamless loops while preserving real-time rendering and free-viewpoint navigation.It operates on casually captured static scenes without dynamic multi-view acquisition or costly physical simulation.Source: §6 · p. 9
- Opacity blending and state offsets are required for seamless loops without noticeable cuts or recurring patterns.The ablation shows cuts when opacity blending is removed and recurring waterfall patterns when state offsets are disabled.Source: Figure 6 · p. 10
- Motion-field refinement reduces unwanted motion in static regions and wrong motion caused by reprojection.The refinement ablation includes static-region motion reduction and view-hit thresholding.Source: Figure 7 · p. 10
- A single directional hint can suffice in some scenes, but waterfall-to-river transitions may require multiple hints; the method also generalizes to lava.The conclusion’s Weir failure case attributes artifacts to inaccurate Gaussian geometry and a poorly reconstructed water surface, which distort reprojected flow.Source: Figure 8 · p. 10, Figure 9 · p. 10, Figure 10 · p. 10
Appendix A: Dense Flow Computation
The appendix describes how sparse flow hints are spread into dense per-view flow maps. The maps are limited to each view’s segmentation mask.
Appendix A: Dense Flow Computation
- Dense flow maps are derived from sparse flow hints by spreading their flow with weighted exponential pixel-distance functions.The passage specifies the L2 Euclidean distance and sets σ = 0.075H.Source: Appendix A · p. 12
- Each pixel’s sparse-flow contribution is weighted by its distance-based function from the hint position, then summed and normalized across hints.The resulting dense flow is defined only for pixels within the view’s segmentation mask.Source: Appendix A · p. 12
- The dense-flow computation uses the hints in each view’s H_n and confines its output to that view’s segmentation mask.The passage defines p_i as the i-th hint position in H_n.Source: Appendix A · p. 12
Appendix B: 3D Motion Field Creation
Algorithm 1 builds a motion field by fusing dynamic-region observations, solving for the field, and refining it with static-region evidence and hit counts.
Appendix B: 3D Motion Field Creation
- The algorithm takes per-view flow, depth, and segmentation inputs and outputs motion field M.The listed inputs are F, D, and S for each view.Source: Appendix B · p. 12
- Dynamic pixels are grouped by voxel to accumulate weighted system terms and track dynamic-pixel and view hits.The accumulated terms are A += JᵀJ and b += Jᵀv, weighted by w.Source: Appendix B · p. 12
- After solving for the field, static-region hits are counted and used with dynamic and view hits to refine it.The refinement uses wstat, wdyn, and wview.Source: Appendix B · p. 12
Appendix C: Motion Field Properties
The appendix characterizes motion fields as sparse after refinement and illustrates how the field deforms an individual Gaussian in symmetric animation.
Appendix C: Motion Field Properties
- The refined motion grid has density at most 5%, and higher-resolution grids do not substantially improve animation quality in the tested scenes.The refinement reduces grid size; initial voxel counts are selected per scene to keep fusion VRAM below 16GB.Source: Appendix C · p. 12
- The symmetric-animation illustration shows forward and backward Gaussian instances and their opacity-independent contours as the motion field deforms the primitive.The instances are shown at different keyframes.Source: Figure 11 · p. 13
Appendix D: Animation Illustration and Ablations
The appendix illustrates Gaussian deformation and examines how transformation settings and keyframe count affect animation quality, memory use, and motion smoothness.
Appendix D: Animation Illustration and Ablations
- Larger α produces convincing fluid-following Gaussian transformations, whereas small α blurs unrealistic deformations and mean-only displacement creates noisy artifacts.The mean-only variant keeps covariance constant; α controls the spread of sigma points around the mean.Source: Appendix D · p. 13, Figure 12 · p. 13
- Reducing keyframes from K = 60 to K = 8 and increasing motion regulation can retain plausible, smooth animation with lower memory consumption.If motion regulation is too large, trajectories may diverge and degenerate; keyframe interpolation maintains smoothness.Source: Appendix D · p. 13
- Table 4 lists per-scene motion-field voxel counts, refined-grid density, average view hits per voxel, and the view-hit threshold.These are the motion-field properties tabulated for the scenes.Source: Table 4 · p. 13
Appendix E: Positional Offsets
Random positional and animation-state offsets create additional Gaussian trajectories that can increase the apparent density of sparsely reconstructed fluid regions, subject to quality trade-offs.
Appendix E: Positional Offsets
- Random positional offsets sampled from a bounded spherical shell create additional forward and backward trajectories, with animation-state offsets varying their timing.The new transformations blend with the original opacity trajectories to preserve looping behavior.Source: Appendix E · pp. 13–14
- Additional offset instances make sparsely reconstructed waterfalls denser and more voluminous than using no positional offset.The comparison is shown in Figure 13.Source: Figure 13 · p. 14
- More than two additional instances can erase animation detail, while greater offset extent can degrade appearance and introduce artifacts.The method supports customization of fluid volume, but these settings bound the useful range.Source: Appendix E · p. 14