SymRegFlow: Symmetry-Regularized Flow Matching for Video World Models

Xi Ye; Yuzhu Wang; Xiaoyang Liu; Jiayi Wang; Yangyang Xu; Ruyu Wang; Wenlin Chen; Duo Su

cs.CVOct 2, 2026

SymRegFlow: Symmetry-Regularized Flow Matching for Video World Models

Authors: Xi Ye, Yuzhu Wang, Xiaoyang Liu, Jiayi Wang, Yangyang Xu, Ruyu Wang, Wenlin Chen, Duo Su,

Organizations: Dept. of Comp. Sci. and Tech., Tsinghua-Bosch Joint ML Center, Tsinghua University · University of Chinese Academy of Sciences · Bosch Center for Artificial Intelligence (BCAI) · Robert Bosch GmbH ·

Abstract

Flow-matching-based multi-view world models generate realistic videos, but are commonly restricted to fixed camera rigs. Extending them to continuously varying camera poses requires paired pose--video observations with dense pose coverage, which are costly to acquire. We introduce SymRegFlow, a symmetry-regularized flow-matching framework for multi-view-consistent video generation across continuous viewpoints without ground-truth novel-view RGB supervision. For each target pose, SymRegFlow geometrically warps source views into noisy anchors and combines masked dual-anchor supervision with cross-anchor denoising-output consistency to mitigate anchor-specific errors. Under an affine Gaussian surrogate, we prove that suitable consistency regularization recovers the clean-reference optimum at fixed noise levels, strictly outperforming single- and merged-anchor baselines. Experiments on Cosmos-Drive-Dreams and nuScenes demonstrate high-quality, multi-view-consistent autonomous-driving video generation: on nuScenes, SymRegFlow achieves the lowest FVD and FVMD among the evaluated baselines, reducing FVD by over 31% relative to the best baseline, and source-conditioned inference also attains the best FID and instance preservation.

Figures & tables

Figure 1: SymRegFlow pipeline. Two observed videos $x^{1},x^{2}$ are independently warped to the same requested novel view, yielding noisy anchors $A^{1},A^{2}$ . The resulting multi-view pseudo-examples are corrupted with shared noise and fed into the same denoiser with directed cross-view attention (DCVA). VAE of latent flow-matching is omitted from the drawing for clarity.

Panel of Figure 2 — Figure 2: $\mathrm{SE}(2)$ MNIST toy study. (a) Viewpoint-dependent noisy anchors $A^{1},A^{2}$ , their mask-weighted fusion $A^{\mathrm{M}}$ , and exact target $x^{\mathrm{n}}$ . (b) SSIM and FD versus novel pose $\alpha$ (top) and base distortion $E_{b}$ (bottom), averaged over five distortion levels and nine poses, respectively. FD denotes pixel-space Fréchet distance on flattened $16\times 16$ pixel features.

Figure 3: Qualitative results on Cosmos-Drive-Dreams. Top: existing and generated novel views at one timestamp. Bottom: novel-view frames and existing-view sequences for seeds 0 and 42.

Method	FID $\downarrow$	FVD $\downarrow$	FVMD $\downarrow$	VBench Subj. $\uparrow$	VBench Bg. $\uparrow$	VBench Flicker. $\uparrow$	VBench IP $\uparrow$	MEt3R $\downarrow$
DiST-4D ( Guo et al., 2025 )	34.59	231.95	5381.67	88.72	91.81	95.67	92.78	0.3362
OmniRe ( Chen et al., 2025 )	44.58	291.99	3104.05	90.20	93.50	95.65	96.11	0.3177
GEN3C ( Ren et al., 2025b )	40.28	289.24	6144.97	88.39	92.66	95.34	37.78	0.3054
FreeVS ( Wang et al., 2025 )	20.60	258.53	4216.99	88.79	91.64	96.04	88.33	0.2829
Ours ( joint-generated )	22.00	158.62	2519.17	90.13	93.32	96.25	96.11	0.2818 †
Ours ( source-cond. )	19.22	159.02	2932.87	90.17	93.32	95.82	99.44	0.2920

Table 1: Novel-view generation on all 30 nuScenes validation scenes at the interpolated midpoint (

\alpha=0.5

) between two observed camera views. VBench scores are multiplied by 100. † MEt3R is computed using generated existing-view videos; other MEt3R scores use captured views. Bold : best; underline : second-best within each column, ranked at full precision.

Figure 4: Qualitative comparison of novel-view synthesis on nuScenes. The last row shows source-cond. SymRegFlow results for a fair comparison with the baselines.

Model	Anchors			DCVA	$\lambda_{c}$	Existing view	Novel view
Model	Left	Right	Merge	DCVA	$\lambda_{c}$	FVD $\downarrow$	FVD $\downarrow$	VBench Subj. $\uparrow$	VBench Bg. $\uparrow$	MEt3R $\downarrow$
Anchor baselines
$A_{L}$	$\checkmark$			$\checkmark$	–	238.14	562.23	87.86	90.36	0.2955
$A_{R}$		$\checkmark$		$\checkmark$	–	198.86	605.63	88.79	92.20	0.3512
$A_{M}$			$\checkmark$	$\checkmark$	–	213.97	704.32	87.71	91.78	0.2787
SymRegFlow variants (ours)

Table 2: Ablation study on four nuScenes scenes.

\lambda_{c}

is the consistency regularization weight (–: not applicable). The superscript ‘FA’ in

C_{0.05}^{\mathrm{FA}}

denotes full attention without DCVA. VBench scores are multiplied by 100. Bold : best; underline : second-best.

Figure 5: Examples of attention bias in anchor baselines. $A_{L}$ and $A_{R}$ copy workers from source-supported regions (cyan boxes) into missing regions (red boxes); green shading indicates anchor-visible regions. The colorbar shows attention strength as a multiple of uniform attention.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Analytic clean-reference excess risk for Proposition 1 at

\alpha\in\{0.35,0.50,0.65\}

. The horizontal baselines use the optimal unregularized predictors; the SymRegFlow curve uses the optimal predictor for each consistency strength (

\lambda

in the plot denotes

\lambda_{c}

). The midpoint makes left/right risks equal, and mirrored viewpoints exchange them. SymRegFlow has zero excess risk at

\lambda_{c}^{\star}=4

and strictly improves on all three baselines in a neighborhood of that strength. These are evaluations of the surrogate formulas, not additional MNIST measurements.

Figure 7: Consistency-weight profiles using the five metrics in Table 2 , normalized against all 11 variants at iteration 2,048. Outward is better. Solid polygons show the 50/50 rank–min–max hybrid, dashed polygons its rank component, and crosses its min–max component. E/N denote existing/novel views; VB denotes VBench. Spoke values follow the table’s precision and scaling (VBench

\times 100

); the mean is the arithmetic average of the five normalized spokes.

Paired anchor	Cross-view route gap $G_{\mathrm{xv}}$			Within-frame mass $P_{\mathrm{U}\rightarrow\mathrm{V}}$
Paired anchor	Single	SymRegFlow	Reduction	Single	SymRegFlow	$\bm{\Delta}$	Relative excess
Left	0.729	0.307	57.8%	0.1745	0.1447	+0.0298	+20.6%
Right	0.865	0.307	64.5%	0.2091	0.1877	+0.0214	+11.4%

Appendix

Table 3: Attention bias in the controlled one-scene overfitting experiment. The cross-view columns report the absolute novel-to-left/right QK route gap

G_{\mathrm{xv}}

(lower is more symmetric), averaged over three relative-offset axes. The within-frame columns report invisible-to-visible attention mass

P_{\mathrm{U}\rightarrow\mathrm{V}}

under an identical paired visibility mask;

\Delta

and the relative excess are single-anchor minus SymRegFlow.

Panel of Figure 8 — Figure 8: Cross-view relative-offset QK profiles for novel-to-left (top) and novel-to-right (bottom) routes. Curves are count-weighted means over valid token pairs and are further averaged over captured denoising steps, DiT blocks, and heads. Single-anchor adaptation preferentially raises compatibility with its fine-tuning source; SymRegFlow reduces this source-dependent route imbalance.

Figure 9: Zero-offset cross-view QK compatibility over denoising. The rightmost panel reports the signed route bias, novel-to-left minus novel-to-right. Its sign follows the fine-tuning anchor for both single-anchor models, while SymRegFlow has a smaller, stable residual imbalance.

Figure 10: SymRegFlow consistency regularization weight sweep against exact held-out rotations (top) and pseudo targets (bottom). The dashed line indicates the selected

\lambda_{c}=2

; stars mark the best sampled weight for each metric. FD denotes pixel-space Fréchet distance on

16\times 16

pixel features.

Figure 11: Qualitative novel-view comparison on nuScenes scene-0012 between the front and front-right cameras.

Figure 12: Qualitative novel-view comparison on nuScenes scene-0013 between the front and front-right cameras.

Figure 13: Qualitative novel-view comparison on nuScenes scene-0014 between the front and front-right cameras.

Figure 14: Qualitative novel-view comparison on nuScenes scene-0014 between the back and back-left cameras.

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Open paper AskPDF arXiv

Flow-matching models generate samples through iterative velocity predictions, but typically do not revisit these predictions using the intermediate representations that produced them. We introduce CorrFlow, a self-correcting flow-matching framework that reuses this information through a lightweight refiner. Under rectified-flow interpolation, the error of the one-step clean prediction equals the realized velocity residual scaled by the noise level. Motivated by this identity, the refiner learns to predict residual corrections from the base model's clean prediction, conditioning, noise level and hidden states from the same forward pass. The correction is added to the base velocity before each sampling update, so subsequent predictions are made from the corrected state. This requires no additional base-model evaluations and only one lightweight refiner evaluation per step. Our theoretical analyses establish conditions under which feature reuse outperforms raw-input affine predictors and refiner training achieves greater residual-risk reduction than continued base-model training under a matched training compute budget. Experiments on class-conditional image generation, text-to-video generation and image-to-video generation show consistent improvements over the corresponding base models, including gains in visual quality and physical consistency. Project Page: https://fogradio.github.io/corrflow-project

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