WaveletGaussian: Efficient Sparse-View 3D Reconstruction

• WaveletGaussian is a framework for efficient sparse-view 3D reconstruction that leverages wavelet-domain frequency separation and diffusion-based repair to address underconstrained geometry.
• It employs a multi-stage pipeline where a coarse 3DGS model is refined using a discrete wavelet transform to separate low-frequency (LL) and high-frequency subbands, with diffusion applied only on the LL subband and a lightweight UNet restoring high-frequency details.
• Empirical results on datasets like Mip-NeRF 360 and OmniObject3D show improved PSNR and reduced training time, highlighting its competitive rendering quality and efficiency over traditional methods.

Searching arXiv for the target paper and closely related wavelet–Gaussian-splatting work. WaveletGaussian is a framework for efficient sparse-view 3D Gaussian object reconstruction that combines 3D Gaussian Splatting (3DGS), wavelet-domain frequency disentanglement, and diffusion-based image repair. It was introduced to address the sharp performance drop of 3DGS in sparse-view settings, where limited observations leave geometry underconstrained and produce severe artifacts in novel-view synthesis. Its central design choice is to move diffusion from RGB image space into the wavelet domain: diffusion is applied only to the low-resolution $LL$ subband, while the high-frequency subbands are refined by a lightweight network. The framework also replaces leave-one-out training-pair curation with an efficient online random masking strategy, with experiments on Mip-NeRF 360 and OmniObject3D reporting competitive rendering quality together with substantially reduced training time (Nguyen et al., 23 Sep 2025).

1. Problem setting and conceptual basis

Sparse-view 3D Gaussian Splatting reconstructs scenes or objects from a small number of 2D images. In this regime, 3DGS is prone to severe artifacts and degraded novel view synthesis because the geometry is underconstrained. Prior work addressed this limitation by employing diffusion models to repair corrupted renders and then using those repaired images as pseudo ground truths for later optimization. According to the reported motivation for WaveletGaussian, such approaches are effective but incur heavy computation from diffusion fine-tuning and repair steps (Nguyen et al., 23 Sep 2025).

WaveletGaussian is organized around three stated premises. First, most image information is concentrated in low frequencies, represented by the $LL$ band in a discrete wavelet transform. Second, the wavelet transform provides a compact, lossless representation that separates low-frequency $(LL)$ and high-frequency $(LH, HL, HH)$ components. Third, applying diffusion only to the $LL$ subband can substantially reduce computational and memory costs while preserving reconstruction capability (Nguyen et al., 23 Sep 2025).

This design places WaveletGaussian at the intersection of two active lines of research. One line uses wavelets to control frequency content in 3DGS training, as in AutoOpti3DGS, which introduces learnable forward and inverse discrete wavelet transforms to restrain Gaussian proliferation during training (Nguyen et al., 29 Jun 2025). Another line uses wavelet factorization to reduce the computational burden of diffusion models by operating on scale-conditioned representations rather than full-resolution images, as in Wavelet Score-based Generative Modeling (Guth et al., 2022). WaveletGaussian combines these themes in the specific context of sparse-view object reconstruction (Nguyen et al., 23 Sep 2025).

2. Architectural organization and reconstruction pipeline

WaveletGaussian is presented as a multi-stage pipeline built around a coarse 3DGS model, wavelet-domain pair construction, frequency-specific restoration modules, and a final refinement stage (Nguyen et al., 23 Sep 2025).

The pipeline begins with coarse training. A 3DGS model $\mathcal{G}_c$ is trained using all $N$ sparse views, but only for a few iterations. The stated purpose is to obtain a rough geometry. Because training is stopped early, even the known views remain moderately corrupted. Renders from $\mathcal{G}_c$ are then transformed into the wavelet domain using a discrete wavelet transform (Nguyen et al., 23 Sep 2025).

The next stage is dataset creation via wavelet DWT and pair curation. Corrupted and clean view pairs are generated for diffusion fine-tuning. Both are DWT-transformed, and only the $LL$ subband is used for the diffusion model $\mathcal{D}$. The high-frequency subbands are handled separately. The training-pair curation is coupled to the online random masking strategy discussed below, which is used to simulate sparse-view corruption patterns efficiently (Nguyen et al., 23 Sep 2025).

In the diffusion fine-tuning and frequency disentanglement stage, the $LL$0 subband pairs train the diffusion model. Because the model operates on the $LL$1 subband, it runs at half the resolution for 2D Haar DWT and learns to inpaint and repair low-frequency, coarse structure. For the high-frequency subbands $LL$2, WaveletGaussian uses a lightweight UNet-like network $LL$3. This network is trained to map the high-frequency subbands of corrupted renders from $LL$4 to those of the clean ground truth. The paper states that these operations are computationally much cheaper because they occur at reduced resolution and channel size (Nguyen et al., 23 Sep 2025).

The final stage is fine training. The coarse model $LL$5 is refined into $LL$6 using pseudo ground truths assembled from the repaired wavelet components. During each training iteration, renders are produced; the $LL$7 subband is repaired by the frozen diffusion model $LL$8; the high-frequency subbands are repaired by the frozen lightweight UNet $LL$9; and an inverse discrete wavelet transform reconstructs improved full-resolution RGB outputs. These reconstructed images are then used as pseudo-ground-truth supervision to continue optimizing $(LL)$0. The stated outcome is to emulate dense-view artifact-free training without requiring dense real views (Nguyen et al., 23 Sep 2025).

A concise representation of the pipeline is as follows.

Stage	Main operation	Role
Coarse training	Train $(LL)$1 for a few iterations	Obtain rough geometry
Wavelet pair creation	DWT of corrupted and clean views	Separate $(LL)$2 from $(LL)$3
Frequency-specific repair	$(LL)$4 on $(LL)$5, $(LL)$6 on high-frequency bands	Restore coarse structure and detail
Fine training	IDWT reconstruction and pseudo-ground-truth supervision	Refine $(LL)$7

This decomposition is frequency-disentangled rather than purely resolution-disentangled. A plausible implication is that the method allocates modeling capacity according to the statistical role of each band: low-frequency structure is handled by diffusion, while high-frequency detail is handled by a smaller deterministic network.

3. Wavelet formulation and loss structure

WaveletGaussian uses Haar DWT to split an image $(LL)$8 into four subbands. The forward transform is given as

$(LL)$9

where $(LH, HL, HH)$0 are low-pass filter matrices and $(LH, HL, HH)$1 are high-pass filter matrices in the row and column directions. Reconstruction is performed by inverse DWT:

$(LH, HL, HH)$2

with perfect reconstruction if filters are appropriately chosen (Nguyen et al., 23 Sep 2025).

The 3DGS optimization itself uses a mixed photometric and perceptual loss,

$(LH, HL, HH)$3

where $(LH, HL, HH)$4 is mean absolute error, $(LH, HL, HH)$5 is a perceptual SSIM loss, and $(LH, HL, HH)$6 is a trade-off hyperparameter (Nguyen et al., 23 Sep 2025).

The wavelet-domain allocation of tasks is explicit. The $(LH, HL, HH)$7 subband carries the diffusion path and is described as the location of core scene content. The $(LH, HL, HH)$8, $(LH, HL, HH)$9, and $LL$0 subbands are treated as high-frequency residual channels for edges and textures. The paper states that repairing only $LL$1 is nearly as effective as RGB repair but much faster, while a lightweight UNet for the high-frequency bands restores details and offsets the drop that occurs when only $LL$2 is repaired (Nguyen et al., 23 Sep 2025).

This wavelet partitioning differs from wavelet-based coarse-to-fine supervision in 3DGS frequency modulation methods. AutoOpti3DGS uses learnable forward and inverse DWT modules to delay the emergence of redundant fine Gaussians during training (Nguyen et al., 29 Jun 2025), whereas WaveletGaussian uses DWT primarily to reduce the cost of diffusion-assisted pseudo-supervision (Nguyen et al., 23 Sep 2025). By contrast, Wavelet-GS applies 3D wavelet decomposition to point clouds and 2D wavelet decomposition to training images within a decoupled optimization framework for scene reconstruction (Zhao et al., 16 Jul 2025). These works share wavelet-based frequency separation, but the operational role of the wavelet transform is different in each case.

4. Online random masking and training-pair curation

A distinctive component of WaveletGaussian is its online random masking (ORM) strategy for generating training pairs. The paper presents ORM as an alternative to the leave-one-out (LOO) strategy commonly used in related sparse-view diffusion pipelines (Nguyen et al., 23 Sep 2025).

Under the LOO baseline, for $LL$3 input views, $LL$4 separate 3DGS models are trained, each leaving out one view as ground truth and predicting that left-out view as corrupted. This simulates realistic sparse-view corruption, but the method is described as highly inefficient because $LL$5 models are trained per object (Nguyen et al., 23 Sep 2025).

ORM instead trains a single 3DGS model $LL$6 on all $LL$7 views. At each iteration, a binary mask $LL$8 is dynamically generated. For each ground-truth view image $LL$9, $\mathcal{G}_c$0 regions are masked; the example value provided is $\mathcal{G}_c$1, covering $\mathcal{G}_c$2 of the object area. The masked regions are drifted via sinusoidal shifts across training epochs, and each training batch uses a different random mask. The model therefore learns to reconstruct from randomly masked inputs while requiring only one model (Nguyen et al., 23 Sep 2025).

The stated benefits of ORM are threefold: massively lower computational cost because only one model is trained instead of $\mathcal{G}_c$3; more diverse corruption patterns, which may improve the robustness of the diffusion fine-tuner; and empirically better performance, since the paper reports that ORM achieves better, higher PSNR than offline masking or LOO together with significantly faster training (Nguyen et al., 23 Sep 2025).

This component addresses a common misconception about diffusion-assisted sparse-view reconstruction: that diffusion efficiency is determined only by the denoiser architecture or sampling resolution. WaveletGaussian treats the curation of corrupted/clean training pairs as an equally important systems bottleneck. That emphasis is explicit in the comparison between ORM and LOO (Nguyen et al., 23 Sep 2025).

5. Empirical results and ablations

WaveletGaussian is evaluated in a 4-view setting on Mip-NeRF 360 and OmniObject3D. The reported comparison includes 3DGS, FSGS, GaussianObject, and WaveletGaussian (Nguyen et al., 23 Sep 2025).

Method	Mip-NeRF 360	OmniObject3D
3DGS	PSNR 20.31, SSIM 0.899, LPIPS 0.108	PSNR 17.29, SSIM 0.930, LPIPS 0.086
FSGS	PSNR 21.07, SSIM 0.910, LPIPS 0.095	PSNR 24.71, SSIM 0.955, LPIPS 0.063
GaussianObject	PSNR 24.81, SSIM 0.935, LPIPS 0.050, 51 mins	PSNR 30.89, SSIM 0.976, LPIPS 0.030, 55 mins
WaveletGaussian	PSNR 25.31, SSIM 0.939, LPIPS 0.047, 33 mins	PSNR 31.22, SSIM 0.983, LPIPS 0.028, 35 mins

On Mip-NeRF 360, WaveletGaussian reports PSNR $\mathcal{G}_c$4, SSIM $\mathcal{G}_c$5, LPIPS $\mathcal{G}_c$6, and $\mathcal{G}_c$7 minutes, compared with GaussianObject at PSNR $\mathcal{G}_c$8, SSIM $\mathcal{G}_c$9, LPIPS $N$0, and $N$1 minutes. The summary in the source describes this as $N$2 PSNR and $N$3 time. On OmniObject3D, WaveletGaussian reports PSNR $N$4, SSIM $N$5, LPIPS $N$6, and $N$7 minutes, compared with GaussianObject at PSNR $N$8, SSIM $N$9, LPIPS $\mathcal{G}_c$0, and $\mathcal{G}_c$1 minutes, summarized as $\mathcal{G}_c$2 PSNR and $\mathcal{G}_c$3 time (Nguyen et al., 23 Sep 2025).

The ablation study examines LOO versus offline random masking versus ORM, diffusion on RGB versus wavelet $\mathcal{G}_c$4 only, and the effect of including or excluding the high-frequency repair network $\mathcal{G}_c$5. The findings reported are that ORM outperforms LOO in speed and sometimes even PSNR; wavelet-domain diffusion alone reduces time but slightly drops detail; and adding the high-frequency repair network restores and even boosts PSNR with only minor overhead, yielding the best overall result (Nguyen et al., 23 Sep 2025).

These empirical trends support the stated claim that the computational bottleneck is reduced because diffusion fine-tuning and repair operate in half resolution and are specialized by frequency band. This suggests that the gain is not merely due to replacing RGB diffusion with lower resolution diffusion, but also due to the explicit decomposition of repair responsibilities across subbands.

6. Relation to adjacent wavelet–Gaussian research

WaveletGaussian belongs to a broader cluster of methods that combine wavelets with Gaussian-based visual representations, but its objective is narrower than several neighboring approaches.

AutoOpti3DGS uses learnable DWT to restrain Gaussian proliferation during 3DGS training. Its coarse-to-fine process begins with high-pass filters initialized to zero so that only coarse image structure is presented early, delaying redundant fine Gaussian formation and producing sparser scene representations (Nguyen et al., 29 Jun 2025). A later extension, Learnable Multi-level Discrete Wavelet Transforms for 3D Gaussian Splatting Frequency Modulation, deepens that curriculum through recursive decomposition of the $\mathcal{G}_c$6 subband and a single scaling parameter for high-pass modulation, further reducing Gaussian counts while maintaining competitive rendering quality (Nguyen et al., 15 Feb 2026). These methods regulate representation growth during training; WaveletGaussian instead reduces the cost of sparse-view pseudo-supervision (Nguyen et al., 23 Sep 2025).

Wavelet-GS applies wavelet decomposition directly to 3D point clouds and 2D sampling, with separate low-frequency and high-frequency branches, voxelization, and a relight module to address global structure, local detail, and lighting artifacts (Zhao et al., 16 Jul 2025). In comparison, WaveletGaussian retains the diffusion-repair paradigm but moves the most expensive stochastic model into the $\mathcal{G}_c$7 band (Nguyen et al., 23 Sep 2025).

The framework also aligns conceptually with wavelet-domain generative modeling. Wavelet Score-based Generative Modeling shows that score-based models can be accelerated by factorizing distributions into wavelet coefficients across scales, with constant step complexity per scale under the stated analysis and overall linear scaling with image size (Guth et al., 2022). WaveletGaussian does not claim that theoretical result, but the use of low-resolution $\mathcal{G}_c$8-only diffusion is consistent with the broader observation that wavelet factorization can regularize or accelerate generative inference (Nguyen et al., 23 Sep 2025, Guth et al., 2022).

A second misconception is that waveletization in 3DGS is primarily about denoising or compression. The nearby literature shows several distinct roles for wavelets: adaptive frequency modulation to control Gaussian densification (Nguyen et al., 29 Jun 2025, Nguyen et al., 15 Feb 2026), decoupled geometry-detail optimization and relighting (Zhao et al., 16 Jul 2025), and low-cost diffusion-based pseudo-supervision for sparse-view reconstruction (Nguyen et al., 23 Sep 2025). “WaveletGaussian” therefore refers not to a generic waveletized Gaussian representation, but to a specific sparse-view object-reconstruction framework whose defining contribution is wavelet-domain diffusion plus online random masking (Nguyen et al., 23 Sep 2025).