GeoFix: Geometry Fixing for 4D Consistent Generation

Yeobin Hong; Hyojun Go; Dohun Lee; Jeongjae Lee; Sunghwan Hong; Federico Tombari; Zhaochong An; Jong Chul Ye

cs.CVOct 9, 2026

GeoFix: Geometry Fixing for 4D Consistent Generation

Authors: Yeobin Hong, Hyojun Go, Dohun Lee, Jeongjae Lee, Sunghwan Hong, Federico Tombari, Zhaochong An, Jong Chul Ye,

Organizations: KAIST · ETH Zürich · Google · EPFL

Abstract

Video diffusion models increasingly serve as priors for 4D generation, but the generated videos often lack geometric consistency. Recent approaches address this through post-training by designing geometric rewards, yet this can degrade texture and fine detail, requiring auxiliary appearance rewards and careful reward balancing. To address this challenge, we propose GeoFix, a unified framework that improves geometric consistency and visual quality with a single geometric reward, applicable to both training and inference-time reward alignment. Our reward measures cross-view depth consistency in static scene regions, targeting structural inconsistencies without directly constraining appearance or penalizing valid object motion. Crucially, depth agreement increases with camera field-of-view overlap even in real videos and 4D datasets, allowing a smaller camera movement to be mistaken for better geometry. We account for this effect by calibrating the reward against the overlap-dependent trend. GeoFix achieves a 39% improvement in WorldScore 3D consistency and a 4% increase in VBench Quality Score.

Figures & tables

Figure 1: Generated 4DGS and rendered videos from GeoFix . Our geometric consistency reward yields more coherent 4D representations through both training and inference-time alignment.

Figure 2: Overview of GeoFix. (a) FOCAL is computed directly from video latents using a stitched 4D reconstructor. (b) We measure cross-view depth reprojection error in static regions and (c) calibrate it to remove overlap bias.

Figure 3: Camera Correlation Analysis. Existing direct and indirect geometric rewards vary with camera movement, creating a bias toward smaller viewpoint changes. Our FOV-calibrated reward remains invariant, providing a more reliable measure of geometric consistency.

Figure 4: Qualitative comparison of 4DGS-rendered Text-to-Video generation.

	$\bm{R_{\mathrm{FOCAL}}}$	WorldScore
		Scene Consistency		Dynamics			Visual Quality		Text Alignment
Method	Avg	3D Cons.	Photo. Cons.	Motion Acc.	Motion Mag.	Motion Smooth.	Style Cons.	Sub. Qual.	Content Align.
Base	29.99	44.39	33.55	50.30	45.17	18.08	84.70	6.80	89.36
SFT	31.02	50.11	38.47	52.76	48.93	19.90	89.00	9.80	87.17
VIST3A	31.06	58.32	47.00	52.84	41.94	25.62	96.63	15.16	95.47
World-R1	30.49	42.26	31.64	51.35	45.90	19.72	88.07	9.57	91.03

Table 1: Quantitative comparison of training-time reward alignment methods.

	VBench
Method	Subject Consistency	Background Consistency	Aesthetic Quality	Imaging Quality	Motion Smoothness
Base	0.9542	0.9528	0.5966	0.6733	0.9841
VGGRPO	0.9644 (+1.07%)	0.9583 (+0.58%)	0.5991 (+0.42%)	0.6861 (+1.90%)	0.9895 (+0.55%)
Base	0.8741	0.9389	0.4679	0.5523	0.9589
Ours	0.9317 (+6.59%)	0.9601 (+2.25%)	0.5272 (+12.67%)	0.5979 (+8.25%)	0.9802 (+2.22%)

Table 2: Quantitative comparison of training-time reward alignment against VGGRPO. Parentheses show relative improvements over the base model.

	Camera Accuracy			WorldScore
				Scene Consistency		Dynamics			Visual Quality		Text Alignment
Method	Rot. Err. $\downarrow$	Trans. Err. $\downarrow$	ATE Norm. $\downarrow$	3D Cons.	Photo. Cons.	Motion Acc.	Motion Mag.	Motion Smooth.	Style Cons.	Sub. Qual.	Content Align.
None	2.040	34.97	0.2563	75.43	76.06	44.81	31.93	23.65	95.47	20.87	94.10
Best-of- $N$	1.751	34.57	0.2507	78.00	78.33	44.59	31.15	24.61	96.08	21.86	94.66
None	2.040	34.97	0.2563	75.43	76.06	44.81	31.93	23.65	95.47	20.87	94.10
DPS	1.977	34.63	0.2562	76.49	76.59	44.42	31.83	23.84	95.56	21.15	94.55

Table 3: Quantitative comparison of inference-time reward alignment.

Figure 5: Qualitative comparison on Image-to-4D generation. We overlay 3D representations from multiple timesteps in a single view to visualize dynamic motion over time.

Figure 6: Quantitative comparison on 4D Scene Generation. Higher is better; axes use different scales.

Figure 7: Analysis of reward sensitivity to geometric corruption.

$\gamma$	VBench Avg.	Dynamic
$0$	0.6802	0.395
$0.7$ (Ours)	0.6861	0.425
$1$	0.6823	0.425

Table 4: Effect of FOV calibration.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Trajectory	Trajectory
Pan Left	Pan Left-Up
Pan Right	Pan Left-Down
Pan Up	Pan Right-Up
Pan Down	Pan Right-Down
Zoom In	Zoom Out

Appendix

Table 5: Ten target camera trajectories used for camera-controlled image-to-4DGS evaluation on 355 VBench-I2V images.

Panel of Figure 9 — Figure 9: Official VideoPhy-2 physical-commonsense (PC) query template used with videophy_2_auto .

Method	Novel Time			Novel View
	PSNR	SSIM	LPIPS $\downarrow$	PSNR	SSIM	LPIPS $\downarrow$
4DGT	17.72	0.5510	0.5032	16.35	0.5015	0.5167
MoVieS	19.12	0.5819	0.3785	16.83	0.4904	0.4271
NeoVerse	20.30	0.5793	0.2917	17.23	0.5117	0.3716
Ours	21.98	0.6451	0.2605	17.65	0.5187	0.3748

Appendix

Table 6: Quantitative comparison on novel-time and novel-view reconstruction.

Figure 10: Additional qualitative results on Text-to-4DGS generation. We overlay 3D representations from multiple timesteps in a single view to visualize dynamic motion over time.

Figure 11: Additional qualitative comparison on Text-to-Video generation.

Figure 12: Overlap bias in cross-view depth errors on reference videos. Reference videos with a large FOV change (low overlap $\Omega$ ) exhibit larger depth reprojection errors than those with a small FOV change (high $\Omega$ ), even when their reconstruction quality is comparable. Thus, the raw depth-agreement score is influenced not only by geometric quality but also by camera motion.

Figure 13: FOV overlap computation. Top: the first camera $C_{1}$ and the last camera $C_{F}$ are expressed in the first camera’s frame, and a reference sphere of radius $r$ is centered at $C_{1}$ . Sphere samples inside the FOV of $C_{1}$ only, of $C_{F}$ only, and of both cameras are shown in blue, orange, and purple, respectively. Bottom: the same samples on the azimuth–elevation grid for (a) small, (b) moderate, and (c) large camera motion between the first and last frames, with the resulting overlap $\Omega$ . The top row corresponds to (b). Insets show the camera poses from above.

Figure 14: Analysis of VBench rewards. (a) Additional qualitative results for the video-quality reward ablation in Section 4.5 , comparing training with VBench rewards against FOCAL. (b) Representative artifacts from optimizing each of the five VBench rewards individually.

Geometric Consistency in Video Generation

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GeoFlow: Enforcing Implicit Geometric Consistency in Video Generation

Jan Ackermann, Shengqu Cai, Boyang Deng, Zhengfei Kuang+2

Stanford University · Google DeepMind

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Generating geometrically consistent videos remains an open challenge: text-to-video diffusion models trained on web-scale data treat geometry only implicitly, leading to object deformation, texture drift, and non-rigid backgrounds under camera motion. Existing solutions either improve consistency as a byproduct, apply only to static scenes or realign the latent space of the model completely. We introduce a geometry-consistency reward that directly measures whether motion in a generated video is compatible with a coherent scene. Our key insight is that in physically consistent videos, background motion should be explainable by rigid camera-induced flow, while independently moving objects should preserve appearance identity along motion trajectories. We operationalize this using optical flow, depth--pose predictions, and feature-based correspondence to separate rigid and dynamic regions and evaluate their respective consistency. Integrating this reward with reinforcement fine-tuning transforms geometric consistency from an emergent property into an explicit optimization objective for video generators. The approach is model agnostic and applies to diverse dynamic scenes containing both camera and object motion. Experiments show substantial reductions in temporal geometric artifacts over strong baselines while preserving perceptual quality. Code and model weights are published.

Abstract

Geometric Consistency in Video Generation

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