HierGF: Hierarchical Gaussian Fields via Geometry-perception Message Passing for Sparse-view 3D Reconstruction

Bi'an Du; Zhimin Zhang; Daizong Liu; Baoquan Chen; Wei Hu

cs.CVOct 1, 2026

HierGF: Hierarchical Gaussian Fields via Geometry-perception Message Passing for Sparse-view 3D Reconstruction

Authors: Bi'an Du, Zhimin Zhang, Daizong Liu, Baoquan Chen, Wei Hu

Organizations: Wangxuan Institute of Computer Technology, Peking University, No. 128, Zhongguancun North Street, Beijing, China · Institute for Math & AI, Wuhan University, Wuhan, 430072, China · School of Intelligence Science and Technology, Peking University, Beijing 100871, China

Abstract

Sparse view 3D reconstruction is an important and common scenario in multimedia applications, such as augmented reality/virtual reality (AR/VR) content creation, cultural heritage digitization, and certain robotic applications, where only a limited number of randomly captured views may be available. However, sparse views contain only limited 3D information, posing two major challenges:1) too few images are available for matching, making it difficult to build multi-view consistency; 2) insufficient view coverage leads to a lack of information in under-sampled regions, resulting in missing parts of object structure. Existing methods mostly still rely on limited reprojection errors and regularization terms, which are prone to overfitting to a single view and inconsistent appearances across views. In geometrically under-sampled regions, they often rely on heuristic density control, lacking reliable guidance and often resulting in blurring and structural holes.To address these issues, this paper proposes Hierarchical Gaussian Fields (HierGF), which revisits sparse-view reconstruction from a hierarchical geometry-perception perspective and converts limited observations into reliable self-generated supervision beyond fixed priors and heuristic density control. In particular, we transform coarse 3D geometric information and additional 2D generative priors into structured pseudo-supervision through a two-stage geometry-perception backbone network, thereby enhancing multi-view consistency with very few input views. In addition, we introduce a learnable confidence network to guide gradients toward cross-view consistent content, and a geometrically consistent densification module to improve the reconstruction of multi-view alignment and under-sampled regions.

Figures & tables

Fig. 1: Motivation of HierGF. (a) Sparse inputs in multimedia scenes provide weak multi-view constraints and leave large regions under-sampled. (b) Existing sparse-view methods rely on fixed regularizers or heuristic generative priors, causing holes and inconsistent textures. (c–d) Our hierarchical pipeline with 2D-assisted perceptual supervision turns few views into reliable pseudo-supervision and produces sharper, more consistent reconstructions than recent Gaussian-based baselines.

Method	Representation path	Diffusion use	Reliability / sparse-region handling	Main distinction from HierGF
3DGS-Enhancer [ 36 ]	Fine-tunes an initial 3DGS	Video diffusion restores rendered novel views	Confidence scores guide enhanced-view fine-tuning	HierGF uses a separate fine field, selective inheritance, and explicit sparse-region completion.
IPSM-Gaussian [ 37 ]	Optimizes 3DGS with diffusion guidance	Inline priors rectify sparse-view score matching	Uses depth/geometric regularization in the IPSM objective	HierGF does not rectify SDS; it refines a selectively initialized fine field with enhanced pseudo-supervision and GCD.
HierGF	Coarse field $\rightarrow$ selectively initialized fine field	Scene-adapted 2D prior enhances coarse-field pseudo-views	Confidence weights filter enhanced losses; GCD allocates Gaussians in sparse regions	Two-field refinement with selective inheritance and coupled perceptual/geometric refinement.

TABLE I: Direct comparison with diffusion-based sparse-view reconstruction methods.

Fig. 2: Overview of the proposed HierGF framework with explicit selective coarse-to-fine transfer and clarified diffusion adaptation. The optimized coarse Gaussian field transfers only spatial means and RGB initialization to the separately optimized fine field, whereas opacity, anisotropic scale, rotation, and higher-order appearance attributes are reinitialized. Only the LoRA adapters are updated during scene-specific diffusion adaptation; the pre-trained SD/ControlNet backbone remains frozen, and the adapted enhancer is frozen during reconstruction.

Component / stage	Data used	Updated parameters	Fixed parameters	Output
Coarse Gaussian optimization	Sparse reference views	Coarse Gaussians	Diffusion module not used	Coarse Gaussian field
Pair construction	Reference views; perturbed coarse renderings	None	Optimized coarse Gaussians	Degraded/reference image pairs
LoRA adaptation	Degraded renderings and reference images	LoRA only	Pre-trained ControlNet/SD v1.5 backbone	Scene-adapted enhancer
Pseudo-view rendering	Additional camera poses	None	Coarse Gaussian field	Coarse pseudo-views
Pseudo-view enhancement	Coarse pseudo-views	None	Diffusion backbone and adapted LoRA	Enhanced pseudo-supervision
Fine-scale optimization	Reference views; enhanced pseudo-supervision	Fine Gaussians; confidence module	Diffusion backbone and adapted LoRA	Final Gaussian representation

TABLE II: Parameter status and data usage in the diffusion-assisted reconstruction pipeline.

Method	4-view			6-view			9-view
Method	LPIPS ∗ ↓	PSNR ↑	SSIM ∗ ↑	LPIPS ∗ ↓	PSNR ↑	SSIM ∗ ↑	LPIPS ∗ ↓	PSNR ↑	SSIM ∗ ↑
DVGO [ 72 ]	24.43	14.39	79.12	26.67	14.30	76.76	25.66	14.74	78.42
3DGS [ 16 ]	10.80	20.31	89.91	8.38	22.12	91.34	6.42	24.29	93.31
DietNeRF [ 52 ]	11.17	18.90	89.71	6.96	22.03	92.86	5.85	23.55	94.24
RegNeRF [ 73 ]	20.44	13.59	84.76	20.72	13.41	84.18	19.70	13.68	85.17
FreeNeRF [ 74 ]	16.83	13.71	85.34	6.84	22.26	93.32	5.51	27.66	94.85

TABLE III: Comparisons on the MipNeRF360 dataset with varying input views. LPIPS ∗ = LPIPS x

10^{2}

and SSIM ∗ = SSIM x

10^{2}

throughout the paper.

Method	4-view			6-view			9-view
Method	LPIPS ∗ ↓	PSNR ↑	SSIM ∗ ↑	LPIPS ∗ ↓	PSNR ↑	SSIM ∗ ↑	LPIPS* ↓	PSNR ↑	SSIM ∗ ↑
DVGO [ 72 ]	14.48	17.14	89.52	12.89	18.32	91.42	11.49	19.26	93.02
3DGS [ 16 ]	8.60	17.29	92.99	7.74	18.29	93.78	6.50	20.26	94.83
DietNeRF [ 52 ]	11.64	18.56	92.05	10.39	19.07	92.67	10.32	19.26	92.58
RegNeRF [ 73 ]	16.75	15.20	90.91	14.38	15.80	92.07	10.17	17.93	94.20
FreeNeRF [ 74 ]	8.28	17.78	94.02	7.32	19.02	94.64	7.25	20.35	94.67

TABLE IV: Comparisons on the OmniObject3D datasets with varying input views.

Fig. 3: Qualitative examples on the MipNeRF360 and OmniObject3D datasets with 4 input views.

Fig. 4: Qualitative examples on the OpenIllumination dataset with 4 input views.

Item	Setting
Representation	Per-scene optimization with a coarse Gaussian field and a separately optimized fine Gaussian field
Camera parameters	Official benchmark intrinsics and extrinsics; fixed during optimization; no camera-pose refinement
SfM initialization input	Selected sparse input views only; no held-out evaluation views
SfM initialization procedure	Sparse feature extraction and exhaustive matching among input views, followed by triangulation under fixed benchmark cameras
SfM filtering settings	Maximum reprojection error $\leq 4$ pixels; minimum triangulation angle $1.5^{\circ}$ ; minimum track length $2$ views
Initial Gaussian attributes	Gaussian centers initialized from triangulated SfM points; RGB initialized from observed colors in input views

TABLE V: Implementation and evaluation settings of HierGF.

Method	4-view			6-view
Method	LPIPS ∗ $\downarrow$	PSNR $\uparrow$	SSIM ∗ $\uparrow$	LPIPS ∗ $\downarrow$	PSNR $\uparrow$	SSIM ∗ $\uparrow$
DVGO [ 72 ]	11.84	21.15	89.73	8.83	23.79	92.09
3DGS [ 80 ]	30.08	11.50	84.54	29.65	11.98	82.77
DietNeRF† [ 52 ]	10.66	23.09	93.61	9.51	24.20	94.01
RegNeRF† [ 73 ]	47.31	11.61	69.40	30.28	14.08	85.86
FreeNeRF† [ 74 ]	35.81	12.21	79.69	35.15	11.47	81.28

TABLE VI: Quantitative comparisons on the OpenIllumination dataset. Methods with †mean the metrics are from the ZeroRF paper [ 4 ] . We follow ZeroRF [ 4 ] on dataset sampling and processing.

Method	Representation	Prior / initialization	Shared benchmarks	Source / scope
HierGF (ours)	Two-field per-scene 3DGS	Sparse SfM; ZoeDepth [ 70 ] ; LoRA-adapted ControlNet [ 68 ] /SD v1.5 [ 69 ]	MipNeRF360, OmniObject3D, OpenIllumination, LLFF, DTU	Ours on one A100; Table V settings
GaussianObject [ 9 ]	Per-scene Gaussian	Visual hull; diffusion-based Gaussian repair	Original shared benchmarks	Reported/Re-run as marked
AugGS [ 81 ]	Two-stage Gaussian reconstruction	Diffusion-enhanced views; structural masks	MipNeRF360, OmniObject3D, OpenIllumination	Related method; compatible entries marked by source
CoR-GS [ 82 ]	Per-scene 3DGS with co-regularization	Co-pruning; pseudo-view co-regularization; method-specific initialization	LLFF, DTU	Public Reported; aligned Re-run when used
NexusGS [ 83 ]	Per-scene 3DGS	Epipolar-depth-guided dense point-cloud initialization	LLFF, DTU	Public Reported; aligned Re-run when used
IPSM-Gaussian [ 37 ]	Diffusion-guided 3DGS optimization	IPSM with depth/geometric regularization	Compatible LLFF and DTU settings	Public reported values marked

TABLE VII: Experimental assumptions of directly related sparse-view reconstruction methods.

Method	Result source	3-view			6-view			9-view
		LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$
IPSM-Gaussian [ 37 ]	Reported	20.70	20.44	70.20	13.50	23.94	81.80	11.10	25.13	85.50
CoR-GS [ 82 ]	Reported	19.60	20.45	71.20	11.50	24.49	83.70	8.90	26.06	87.40
NexusGS [ 83 ]	Reported / Re-run	17.70	21.07	73.80	10.65	24.83	84.92	8.35	26.24	88.00
HierGF (ours)	Ours	17.05	21.28	74.45	10.10	25.03	85.42	7.97	26.39	88.37

TABLE VIII: Quantitative comparison on LLFF under 3-view, 6-view, and 9-view settings.

Method	Result source	3-view			6-view			9-view
		LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$
IPSM-Gaussian [ 37 ]	Reported	12.10	19.99	85.60	–	–	–	–	–	–
CoR-GS [ 82 ]	Reported	11.90	19.21	85.30	6.80	24.51	91.70	4.50	27.18	94.70
NexusGS [ 83 ]	Reported / Re-run	10.20	20.21	86.90	6.15	24.91	92.25	4.15	27.38	95.05
HierGF (ours)	Ours	9.68	20.40	87.45	5.74	25.10	92.68	3.89	27.52	95.36

TABLE IX: Quantitative comparison on DTU under 3-view, 6-view, and 9-view settings.

Fig. 5: Qualitative comparison on LLFF under the 3-view setting. Representative held-out views from fern , orchids , room , and fortress are shown. Columns compare the ground truth, IPSM-Gaussian, CoR-GS, NexusGS, and HierGF at aligned viewpoints; enlarged crops emphasize thin structures, boundaries, texture details, and weakly observed regions.

Fig. 6: Qualitative comparison on DTU under the 3-view setting. Representative held-out views from scans 34, 40, 103, and 8 are shown. Columns compare the ground truth, IPSM-Gaussian, CoR-GS, NexusGS, and HierGF at aligned viewpoints; enlarged crops emphasize object contours, fine geometry, surface texture, and sparsely observed regions.

Fig. 7: Ablation study on the two-stage hierarchical backbone. From top to bottom, Coarse-only, Fine-only, Single-GF Joint, and Full HierGF are shown.

Fig. 8: Ablation study on geometry-consistent densification. Red boxes highlight that our full model better preserves thin structures and closes gaps in under-sampled regions.

Setting/Dataset	MipNeRF360			OmniObject
Setting/Dataset	LPIPS ∗ ↓	PSNR ↑	SSIM ∗ ↑	LPIPS ∗ ↓	PSNR ↑	SSIM ∗ ↑
Coarse-only	9.76	19.63	88.90	7.92	17.88	94.35
Fine-only	8.12	21.84	91.03	6.84	20.59	95.01
Single-GF Joint	5.24	25.06	92.95	3.43	27.06	96.90
Full HierGF	3.85	28.48	95.87	1.76	34.08	98.36

TABLE X: Ablation study over HierGF’s hierarchical architecture on the MipNeRF360 and OmniObject datasets with 4 input views.

Components			Metrics
SPS	VCS	PCS	LPIPS ∗ $\downarrow$	PSNR $\uparrow$	SSIM ∗ $\uparrow$
			9.40	20.33	89.78
✓			5.06	25.73	92.18
✓	✓		4.71	27.62	93.04
✓		✓	3.13	28.09	95.26
✓	✓	✓	3.85	28.48	95.87

TABLE XI: Ablation study over 2D-assisted Perceptual Enhancement on the MipNeRF360 and dataset with 4 input views. SPS , VCS , and PCS represent self-generated perceptual supervision, view-level confidence supervision and pixel-level confidence supervision, respectively.

Fine-field initialization strategy	Transferred parameters from coarse field	MipNeRF360			OmniObject3D
		LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$
Reinitialize all attributes	None	4.46	27.21	94.67	2.21	31.65	97.53
Transfer all attributes	$\mu,q,s,\sigma,\mathrm{SH}$	4.18	27.82	95.14	1.98	32.93	97.95
Selective transfer, HierGF	$\mu$ and RGB only	3.85	28.48	95.87	1.76	34.08	98.36

TABLE XIII: Controlled ablation of the coarse-to-fine parameter-transfer rule under the 4-view setting.

Setting	MipNeRF360			OmniObject3D
	LPIPS ${}^{*}\downarrow$	PSNR $\uparrow$	SSIM ${}^{*}\uparrow$	LPIPS ${}^{*}\downarrow$	PSNR $\uparrow$	SSIM ${}^{*}\uparrow$
Full HierGF w/o ZoeDepth	4.29	27.72	95.01	1.91	33.43	98.02
Full HierGF	3.85	28.48	95.87	1.76	34.08	98.36

TABLE XIV: Controlled ablation of ZoeDepth supervision under the 4-view setting.

Setting	LPIPS ${}^{*}\downarrow$	PSNR $\uparrow$	SSIM ${}^{*}\uparrow$
Reference views only; no pseudo-view supervision	10.07	19.86	89.05
Raw pseudo-views; no diffusion enhancement or confidence weighting	9.40	20.33	89.78
Frozen pre-trained 2D prior; without LoRA adaptation or confidence weighting	5.73	24.86	91.64
LoRA-adapted enhanced pseudo-views (SPS); without confidence weighting	5.06	25.73	92.18
SPS + view-level confidence supervision (VCS)	4.71	27.62	93.04
SPS + pixel-level confidence supervision (PCS)	3.13	28.09	95.26

TABLE XV: Controlled ablation of pseudo-view supervision, the diffusion prior, LoRA adaptation, and confidence weighting on MipNeRF360 under the 4-view setting.

Radius setting	Radius value	MipNeRF360			OmniObject3D
		LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$
Small radius	$1.5s_{v}=0.03D_{\mathrm{rob}}$	4.16	28.17	94.82	1.86	33.72	98.04
Default radius	$2.0s_{v}=0.04D_{\mathrm{rob}}$	3.85	28.48	95.87	1.76	34.08	98.36
Large radius	$3.0s_{v}=0.06D_{\mathrm{rob}}$	4.04	28.28	95.18	1.83	33.89	98.18

TABLE XVI: Ablation study on the neighborhood radius

r

under the 4-view setting.

Setting	MipNeRF360			OmniObject3D
	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$	LPIPS* $\downarrow$	PSNR $\uparrow$	SSIM* $\uparrow$
w/o GCD, standard ADC	4.58	27.96	93.37	1.93	31.07	97.56
Distance-only interpolation	4.02	28.25	94.92	1.79	33.74	98.05
Additive: $w_{\mathrm{normal}}+w_{\mathrm{distance}}$	3.95	28.34	95.31	1.78	33.91	98.18
Multiplicative: $w_{\mathrm{normal}}\cdot w_{\mathrm{distance}}$	3.85	28.48	95.87	1.76	34.08	98.36

TABLE XVII: Comparison of weighting strategies in geometry-consistent densification under the 4-view setting.

Method	Recon. time (s) $\downarrow$	Recon. speedup	Rendering time (s) $\downarrow$	Rendering speedup
ZeroRF [ 4 ]	1309	$2.07\times$	78	$1.11\times$
GaussianObject [ 9 ]	7028	$11.12\times$	89	$1.27\times$
WaveletGS [ 76 ]	1800	$2.85\times$	95	$1.36\times$
HierGF (ours)	632	–	70	–

TABLE XVIII: Efficiency comparison on the MipNeRF360 kitchen scene under the 4-view setting. All methods are evaluated at

779\times 520

on a single NVIDIA A100 GPU. The speedup values are calculated relative to HierGF.

Fig. 9: Stage-wise runtime breakdown of HierGF on the MipNeRF360 kitchen scene under the 4-view setting. Gaussian optimization remains the dominant cost, while diffusion-related processing is used only during reconstruction.

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