GeoNaviDiff: Transferring Disentangled Semantic Controls to Diffusion Features via Local Riemannian Navigation

Tao Sun; Huanting Guo; Baao Xie; Zhou Fang; Qiuyu Chen; Hao Zheng; Wenjun Zeng

cs.CVOct 19, 2026

GeoNaviDiff: Transferring Disentangled Semantic Controls to Diffusion Features via Local Riemannian Navigation

Authors: Tao Sun, Huanting Guo, Baao Xie, Zhou Fang, Qiuyu Chen, Hao Zheng, Wenjun Zeng

Organizations: Ningbo Key Laboratory of Spatial Intelligence and Digital Derivative, Ningbo Institute of Digital Twin, Eastern Institute of Technology, Ningbo, Zhejiang 315200, P.R. China · Beijing Institute of Technology, Beijing, P.R. China · Shaanxi Normal University

Abstract

Disentangled real-image manipulation requires factor-specific semantic control while preserving image fidelity and non-target content. StyleSpace $S$ provides interpretable controls but is limited by GAN inversion, whereas diffusion models offer stronger image realization without an explicit factorized control basis. We introduce GeoNaviDiff, an unsupervised cross-space framework that transfers disentangled StyleSpace interventions to local Riemannian trajectories in diffusion $h$ -space. GeoNaviDiff constructs reconstruction-decoupled supervision by extracting a spherical Log-map tangent from a matched StyleGAN reconstruction-edit pair and parallel-transporting it to the real-image diffusion state. A shared, factor-conditioned Navigator predicts this tangent at inference, while norm-preserving geodesic realization and source-anchored rollout stabilize the reverse process without edited references or factor-specific models. Experiments across multiple datasets show that GeoNaviDiff outperforms the compared methods in fidelity, factor selectivity, edit locality, and trajectory smoothness.

Figures & tables

Figure 1: Conceptual comparison of Euclidean, arbitrary geodesic, and GeoNaviDiff trajectories in diffusion $h$ -space.

Figure 2: Training framework of GeoNaviDiff. (a) Unsupervised semantic discovery and disentangled control construction in $\mathcal{S}$ -space, followed by cross-space navigation into diffusion $h$ -space. (b) The four-step parallel-transport procedure is used to construct the tangent navigation target.

Method	FFHQ				AFHQ-v2				Stanford Cars
Method	FID $\downarrow$	PPL $\downarrow$	OFlow $\downarrow$	DCI $\uparrow$	FID $\downarrow$	PPL $\downarrow$	OFlow $\downarrow$	DCI $\uparrow$	FID $\downarrow$	PPL $\downarrow$	OFlow $\downarrow$	DCI $\uparrow$
$\beta$ -TCVAE ( Chen et al. 2018 )	96.50 $\pm$ 2.40	128.85	0.12	0.28	72.00 $\pm$ 2.17	132.69	0.13	0.32	92.78 $\pm$ 2.35	133.54	0.13	0.31
FactorVAE ( Kim and Mnih 2018 )	104.80 $\pm$ 2.88	118.37	0.11	0.36	84.50 $\pm$ 2.60	122.56	0.14	0.35	115.48 $\pm$ 3.52	120.78	0.12	0.40
e4e ( Tov et al. 2021 )	75.74 $\pm$ 1.49	130.45	0.30	0.36	26.65 $\pm$ 0.55	142.69	0.23	0.31	84.08 $\pm$ 1.93	147.28	0.34	0.42
SFE ( Bobkov et al. 2024 )	76.42 $\pm$ 1.35	114.88	0.17	0.54	31.84 $\pm$ 1.12	125.71	0.19	0.49	79.21 $\pm$ 1.70	122.75	0.27	0.47
NaviGAN ( Cherepkov et al. 2021 )	76.31 $\pm$ 1.24	94.33	0.10	0.60	49.36 $\pm$ 1.09	88.95	0.12	0.57	53.60 $\pm$ 0.92	93.57	0.13	0.62

Table 1: Comparison with existing methods across VAE-, GAN-, and diffusion-based generative models.

\dagger

denotes our baseline, bold indicates the best result, and “–” denotes not measured. Asyrp lacks fixed latent codes for PPL and DCI.

Figure 3: Qualitative comparison on smile manipulation across traversal levels.

Figure 4: Qualitative traversals of GeoNaviDiff across datasets and semantic factors.

Figure 5: Stepwise ablation of cross-space navigation, Riemannian realization, and source-anchored rollout.

Image Editing

Image editing changes selected visual content while preserving the parts of an image that should remain unchanged.

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Despite the generative capabilities of diffusion and flow models, real-image editing remains constrained by a persistent trade-off between semantic editability and structural fidelity. We trace a primary cause of this limitation to the implicit coupling of edit progress with model scale in existing paradigms. Under this coupling, stronger edits typically require visiting noisier states, which spends computation on destabilizing layout before the semantic change is well localized. We introduce NaviEdit, a training-free inference-time controller that decouples edit progress from model scale traversal through a strict self-consistency contract. NaviEdit operates at the rollout level and leaves the underlying pretrained model unchanged. It treats scale as a control input and reallocates a fixed step budget toward semantically responsive intermediate scales instead of destructive high-noise regimes. Experiments show positive average gains across compatible editors and flow backbones, supporting decoupling as a portable inference-time control principle.

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