Research map / 3D vision / Gaussian splatting
Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle
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Gaussian-Flow models dynamic scenes by explicitly deforming each 3D Gaussian's position, rotation, and color with a polynomial plus Fourier-series residual (DDDM), enabling fast training and real-time rendering without neural networks.
Problem
Fast, high-quality 4D (dynamic) scene reconstruction and real-time rendering from multi-view and monocular videos, where NeRF-based methods are slow and per-frame 3DGS is storage-heavy and inapplicable to monocular input.
Approach
A Dual-Domain Deformation Model fits each Gaussian's time-dependent attribute residuals with a joint polynomial (time domain) and Fourier series (frequency domain), with adaptive timestamp scaling and KNN-rigid plus time-smoothness regularizers, avoiding any neural network in the deformation.
Key results
- On D-NeRF synthetic scenes Gaussian-Flow reaches 34.27 PSNR versus 33.30 for 4D-GS.
- On HyperNeRF vrig scenes it reaches 25.6 mean PSNR at 30K steps (7 min training, 125 FPS) and 26.3 at 60K steps.
- On the Plenoptic Video dataset it reaches 30.5 PSNR at 30K steps (22.5 min) and 32.0 PSNR at 60K steps (41.8 min).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add KNN rigid regularization and time smoothness regularization together (ablation) | Gaussian-Flow · HyperNeRF vrig | PSNR: full model 29.92 vs 28.48 without KNN rigid and 29.12 without time smooth | Helped |
| Add DDDM (hybrid polynomial + Fourier) over polynomial-only or Fourier-only deformation (ablation) | Gaussian-Flow deformation model · monocular and multiview scenes | qualitative rendering quality | Helped |
| Increase Fourier/DDDM order from 8 up to 16 then 32; going to 64 drops (ablation) | Gaussian-Flow DDDM · HyperNeRF | PSNR: peak at order 16 (29.9); order 64 gives 27.8 | Mixed |
| Replace per-frame 3DGS with DDDM deformation of Gaussians | 3DGS for dynamic scenes · Plenoptic Video | training time: 22.5 min vs hours for DyNeRF and K-Planes (1.8 hours) | Helped |
| Use DDDM explicit deformation on Plenoptic Video at 30K steps versus prior methods | Gaussian-Flow · Plenoptic Video | PSNR: 30.5 at 30K, below K-Planes 31.6, but 32.0 at 60K | Mixed |
| Use DDDM explicit deformation on HyperNeRF vrig scenes | Gaussian-Flow · HyperNeRF vrig | PSNR: 26.3 (60K) vs 24.3 TiNeuVox best prior baseline | Helped |
Surprising findings
- Increasing the Fourier series order beyond 32 degrades performance, attributed to over-parameterization of the deformation model.
- The method struggles to preserve thin structures such as the 3D printer thread.
Limitations
- Difficulty maintaining high-fidelity thin structures such as the 3D printer thread.
- Deformation model may not capture fine details in scenes with complex motion patterns.
Experimental setup
Datasets: D-NeRF synthetic blender HyperNeRF Plenoptic Video dataset
Benchmarks: D-NeRF synthetic blender HyperNeRF vrig Plenoptic Video
Metrics: PSNR SSIM LPIPS training time FPS
Baselines: TiNeuVox K-Planes 4D-GS NeRFPlayer DyNeRF HyperNeRF Nerfies NeRF
Builds on: 3D Gaussian Splatting HyperNeRF D-NeRF
Closest papers by meaning
- Fully Explicit Dynamic Gaussian Splatting (NeurIPS 2024 · similarity 0.92)
- H3D-DGS: Exploring Heterogeneous 3D Motion Representation for Deformable 3D Gaussian Splatting (NeurIPS 2025 · similarity 0.92)
- DGS-LRM: Real-Time Deformable 3D Gaussian Reconstruction From Monocular Videos (NeurIPS 2025 · similarity 0.92)
- Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction (CVPR 2024 · similarity 0.92)
- 4D Gaussian Splatting for Real-Time Dynamic Scene Rendering (CVPR 2024 · similarity 0.92)
- Motion Decoupled 3D Gaussian Splatting for Dynamic Object Representation (AAAI 2025 · similarity 0.91)
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