Dragging with Geometry: From Pixels to Geometry-Guided Image Editing

## Abstract

Abstract Interactive point-based image editing serves as a controllable editor, enabling precise and flexible manipulation of image content. However, most drag-based methods operate primarily on the 2D pixel plane with limited use of 3D cues. As a result, they often produce imprecise and inconsistent edits, particularly in geometry-intensive scenarios such as rotations and perspective transformations. To address these limitations, we propose a novel geometry-guided drag-based image editing method—GeoDrag, which addresses three key challenges: 1) incorporating 3D geometric cues into pixel-level editing, 2) mitigating discontinuities caused by geometry-only guidance, and 3) resolving conflicts arising from multi-point dragging. Built upon a unified displacement field that jointly encodes 3D geometry and 2D spatial priors, GeoDrag enables coherent, high-fidelity, and structure-consistent editing in a single forward pass. In addition, a conflict-free partitioning strategy is introduced to isolate editing regions, effectively preventing interference and ensuring consistency. Extensive experiments across various editing scenarios validate the effectiveness of our method, showing superior precision, structural consistency, and reliable multi-point editability. The code will be available on https://github.com/xinyu-pu/GeoDrag .

## 1 Introduction

Image editing [1, 2, 3] has seen remarkable progress in recent years, largely driven by the emergence of powerful generative models [4, 5, 2, 6, 7]. Among these, text-guided image editing [8, 9, 7, 10] has become a widely adopted paradigm, allowing users to modify images using natural language prompts. While expressive and flexible, this approach often falls short in providing fine-grained spatial control—especially when precise, localized, or geometry-sensitive edits are required [11, 3, 12, 13, 14, 15, 16].

To overcome these limitations, point-based image editing [11, 3, 12, 13, 14, 15, 16] has emerged as a powerful alternative, gaining traction for its user-friendly, precise manipulation. By enabling users to specify handle-to-target point pairs, methods such as DragGAN [11] and its successors [3, 12, 13, 14, 15, 16, 17] offer intuitive and precise image manipulation. They often adopt a two-step pipeline: (1) motion supervision, dragging the handle point toward the target, and (2) point tracking, monitoring the handle’s updated position during editing.

Motivation. Despite their success, existing point-based methods often rely on iterative gradient-based optimization, which is computationally intensive and impractical for real-time use. To improve efficiency, recent approaches like FastDrag [18] and RegionDrag [19] propose one-step editing via latent relocation based on dense displacement fields constructed over user-specified regions. However, these methods operate purely in the 2D pixel plane, and ignore the underlying 3D scene geometry. This becomes a critical limitation for complex transformation or geometry-intensive edits—like rotations or perspective shifts—where 2D-only reasoning leads to structural artifacts, unnatural deformations, and spatial misalignment. For example, plane-aware strategy decays displacement strength based solely on pixel distance, and ignores 3D geometry, resulting in perceptual distortions of human’s face as shown in Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1)(a, left).

Figure: Figure 1: (a) Displacement fields. Left: Plane-based estimation (e.g., FastDrag [18]) lacks geometric awareness and introduces structural inconsistencies under geometry-intensive edits like rotation. Right: Our geometry-aware GeoDrag aligns with 3D structure—near pixels move more, far pixels less. (b) Relying solely on 3D geometry can produce discontinuous displacements near object boundaries. (c) Two nearby handle-target pairs with opposing directions (e.g., leftward and rightward drags) may conflict, causing displacement cancellation and editing failure. The color legend (Shift/Distance/Depth) is provided in Appendix [H](https://arxiv.org/html/2509.25740v1#A8).
Refer to caption: x1.png

To improve the realism and semantic consistency of image editing, incorporating 3D geometric information is essential, as it offers richer structural cues beyond the 2D pixel plane. However, this introduces three key challenges.
1) How can geometry be integrated into pixel-level editing? While 3D cues (e.g., depth maps) are informative, they do not align directly with pixel-wise operations. For example, a drag defined in the image plane may become ambiguous in 3D due to perspective and depth variation—highlighting the need for a mechanism to incorporate geometry into 2D editing pipelines.
2) Is geometry alone sufficient for high-quality editing? Although helpful for preserving global structure, geometry alone may cause issues. Displacement fields based solely on 3D geometry (e.g., depth) often become discontinuous near object boundaries (see Sec. [3.1](https://arxiv.org/html/2509.25740v1#S3.SS1)), disrupting the diffusion process and causing semantic artifacts as shown in Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1)(b).
3) How to reconcile guidance from multiple handle-target pairs? In real scenarios, users often specify multiple drag points. If their displacement fields overlap—especially with opposing directions—they can destructively interfere, even with distance-based weighting as in FastDrag [18]. This leads to displacement cancellation and failed edits as illustrated by Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1)(c). These challenges call for a unified framework that integrates 3D geometry and 2D cues while resolving conflicts for precise and coherent manipulation.

Contributions.
To tackle these challenges, we propose GeoDrag—a drag-based image editing framework that is both geometry-aware and plane-aware, ensuring coherent, high-fidelity, and fast one-step image manipulation. Built upon the latent consistency model (LCM) [20], GeoDrag predicts a dense displacement field directly in the noisy latent space at a specific diffusion timestep—circumventing iterative optimization and enabling fast and efficient editing. GeoDrag introduces three key innovations to resolve the above three challenges, respectively.
1) Geometry-aware field modeling: To resolve the mismatch between 3D geometry and 2D editing, GeoDrag introduces a novel influence function that modulates displacement strength based on 3D geometric relationships. By leveraging depth contrast, it ensures that nearby regions undergo stronger projective motion, while distant areas move more subtly—preserving 3D structure (see the well-edited human face in Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1)(a, right)). 2) Spatial plane modulation: Addressing the limitations of using 3D geometry alone, GeoDrag incorporates a spatial influence function based on 2D pixel plane. This improves local structure preservation and editing precision, especially in flat or geometry-ambiguous regions. 3) Conflict-Free Partitioning: To mitigate conflicts in multi-point editing, GeoDrag segments the editing mask into non-overlapping sub-regions, each associated with its nearest handle point. Independent displacement fields are computed per region, avoiding destructive interference and ensuring coherent multi-point manipulation. Together, these contributions allow GeoDrag to perform fast, high-quality, and semantically consistent edits in a single step—advancing the state of controllable, geometry-aware image manipulation.

Figure: Figure 2: Experimental Comparison. (a) Representative edits across diverse scenarios. (b) Quantitative results on DragBench: lower MD and DAI indicate more accurate editing. (c) Runtime and memory comparison across our GeoDrag and previous SoTAs.
Refer to caption: x2.png

Extensive experiments verify the effectiveness and efficiency of GeoDrag. As shown in Fig. [2](https://arxiv.org/html/2509.25740v1#S1.F2), we provide a three-part visualization: (a) Visual Quality – GeoDrag delivers high-quality edits across challenging scenarios, including multi-point editing (e.g., bulb), structure-preserving deformation (e.g., mountain), localized manipulation (e.g., lion’s mouth), and geometry-aware tasks (e.g., face rotation); (b) Quantitative Results – GeoDrag achieves superior alignment accuracy, improving runner-up’s dragging accuracy index metric (DAI) by 1.4x and mean distance metric (MD) by 1.1x; (c) Efficiency – GeoDrag offers a favorable trade-off between speed and memory. While its runtime gain is modest, it remains lightweight and highly competitive due to its strong editing performance.

## 2 Related Work

Text-Based Image Editing.
Text-based image editing manipulates images via natural language prompts. Gal *at al.* [21] utilize textual inversion for personalized generation by embedding user-specific concepts. DiffusionCLIP [22] fine-tunes diffusion models with CLIP supervision, while Prompt-to-Prompt [4] achieves train-free editing by modifying cross-attention maps. Null-text inversion [2] optimizes unconditional text embeddings for faithful reconstruction of real images. Imagic [5] interpolates between text and image-specific embeddings but requires per-task tuning. Other approaches like CycleDiffusion [23] and DDPM inversion [9] explore latent spaces to support high-quality editing. InstructPix2Pix [24] trains on instruction-image pairs, enabling direct prompt-driven editing. RPG [6] introduces a multimodal LLM for reasoning and planning editing. Despite their flexibility, text-based methods often lack spatial precision and fine-grained control, limiting their applicability for detailed editing tasks.

Interactive Point-Based Image Editing.
Point-based methods enable precise manipulation by directly dragging image elements. DragGAN [11] introduced this paradigm with GANs, later improved by diffusion-based approaches [25, 26, 20] like DragDiffusion [3], which integrates motion supervision and identity-preserving fine-tuning. Extensions enhance usability (EasyDrag [14]), stability (FreeDrag [13]), semantic control (DragNoise [12]), or robustness (GoodDrag [15], StableDrag [27]). To boost efficiency, FastDrag [18], RegionDrag [19], and SDEDrag [28] use lightweight latent manipulations, while DragonDiffusion [29], DiffEditor [30], and InstantDrag [17] introduce energy-based or real-time formulations. Despite progress, they remain limited to 2D pixel reasoning, restricting realism in geometry-sensitive edits. We address this with GeoDrag for controllable, structure-preserving, and efficient image editing. In parallel, FlowDrag [31] uses mesh reconstruction and iterative deformation to improve editing quality, but at a higher computational cost, that limits its responsiveness. By contrast, GeoDrag achieves geometry-consistent control while remaining responsive for interactive editing.

## 3 Methodology

Figure: Figure 3: Overall framework of GeoDrag. In drag pipeline, the mask is split into sub-regions, each with a pair of drag points. For each sub-region, the geometry- and plane-aware displacement fields are independently calculated (see Sec. [3.1](https://arxiv.org/html/2509.25740v1#S3.SS1) and Sec. [3.2](https://arxiv.org/html/2509.25740v1#S3.SS2)). Subsequently, these fused fields are aggregated without conflict (see Sec. [3.3](https://arxiv.org/html/2509.25740v1#S3.SS3)). The final field enables one-step editing via latent relocation and interpolation, with reference guidance to preserve semantics.
Refer to caption: x3.png

We begin by formalizing the task of interest. Given an image and a set of $k$ point pairs $\{(\boldsymbol{h}_{i},\boldsymbol{t}_{i})\}_{i=1}^{k}$, where each $\boldsymbol{h}_{i}$ is a handle point and $\boldsymbol{t}_{i}$ its corresponding target, the goal is to move each $\boldsymbol{h}_{i}$ toward $\boldsymbol{t}_{i}$ while preserving semantic consistency and visual realism. Recent efficient methods such as FastDrag [18] and RegionDrag [19] enable a fast one-step editing by computing a displacement field $\boldsymbol{f}\in\mathbb{R}^{H\times W\times 2}$, which warps the latent $\boldsymbol{z}_{T}$ at timestep $T$ via forward mapping:

$$ $\boldsymbol{z}^{*}_{T(i+f_{i,j,1},j+f_{i,j,0})}=\boldsymbol{z}_{T(i,j)}.$ (1) $$

Each $\boldsymbol{f}_{i,j}=(f_{i,j,1},f_{i,j,0})$ defines how much the latent feature at spatial location $(i,j)$ should be shifted along the x and y axes in the image. Next, the modified latent $\boldsymbol{z}^{*}_{T}$ is then passed into a well-trained diffusion model to generate the edited image.

Existing methods [18, 19, 28] construct $\boldsymbol{f}$ using only 2D pixel-plane heuristics, ignoring the underlying 3D structure. This estimated $\boldsymbol{f}$ often leads to unrealistic deformations, semantic breaks, and perspective issues—especially in geometry-sensitive edits like rotations or viewpoint shifts (see Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1) (a)). Additionally, multiple handle-target pairs can create overlapping and conflicting displacement fields, causing inconsistent guidance and editing failures (see Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1) (c)).

To address these issues, we propose GeoDrag which jointly leverages 3D geometry and 2D spatial priors to produce accurate and coherent displacement fields. As illustrated in Fig. [3](https://arxiv.org/html/2509.25740v1#S3.F3), GeoDrag consists of three components: (1) a geometry-aware field modeling module that adjusts motion strength using depth cues; (2) a spatial plane modulation that combines 3D and 2D guidance; and (3) a conflict-free partitioning that decomposes the editing mask to resolve conflicting drag signals. These components respectively resolve three fundamental challenges associated with geometry-aware drag-based editing, and they together enable high-quality and geometry-consistent image edits in a single step. Moreover, to avoid the over-smoothing often introduced by interpolation, we further refine the interpolated latents with a masked stochastic DDIM update, which injects randomness only inside the interpolated region while keeping the rest deterministic. Formally, given a binary mask $\boldsymbol{M}$ indicating the interpolated area, the sample step is

$$ $\boldsymbol{z}^{*}_{t-1}=\sqrt{\bar{\alpha}_{t-1}}\hat{\boldsymbol{z}^{*}_{0}}+\sqrt{1-\bar{\alpha}_{t-1}-\sigma_{t}^{2}\odot\boldsymbol{M}}\,\epsilon_{\theta}(\boldsymbol{z}^{*}_{t},t)+\sigma_{t}\,(\epsilon\odot\boldsymbol{M}).$ (2) $$

This post-interpolation refinement preserves global coherence, effectively alleviating blur without incurring extra sampling overhead. Below, we elaborate on these three components and their resolved challenges in turn. Specifically, we focus on the case of a single handle-target pair in Sec. [3.1](https://arxiv.org/html/2509.25740v1#S3.SS1) and Sec. [3.2](https://arxiv.org/html/2509.25740v1#S3.SS2), and extend the approach to multi-point editing in Sec. [3.3](https://arxiv.org/html/2509.25740v1#S3.SS3).

### 3.1 Geometry-Aware Field Modeling

Incorporating 3D geometry into 2D image editing poses a key challenge: pixel-level operations on the image plane do not directly correspond to transformations in 3D space. For instance, applying the same 3D displacement to different points can lead to inconsistent 2D motions due to perspective distortion and depth variation. To bridge this gap, our core idea is to project 3D displacements into the image plane while preserving 3D structure information. Accordingly, we design a geometry-aware influence function that converts 3D drag displacements into pixel plane by incorporating relative depth between pixels and the handle point. This strategy ensures that pixels respond to the displacement in a depth-consistent manner: pixels with lower depth to handle point are influenced more, while those at larger depths move less. By aligning the 2D displacement strength with 3D proximity, the method preserves the consistency of the 3D structure during 2D “dragging”, avoiding spatial tearing or inconsistent deformation on the image plane.

Specifically, consider a drag operation applied to 3D space $(x,y,z)$ with a 3D displacement vector $(\delta x,\delta y,\delta z)$. Given a camera intrinsic $\mathbf{K}$ which in unknown in this work, the corresponding projected 2D coordinate $(u,v)$ on the image plane can be computed as follows:

$$ $z\left[\begin{matrix}u\\ v\\ 1\end{matrix}\right]=\mathbf{K}\left[\begin{matrix}x\\ y\\ z\end{matrix}\right]=\left[\begin{matrix}f_{x}&0&c_{x}\\ 0&f_{y}&c_{y}\\ 0&0&1\end{matrix}\right]\left[\begin{matrix}x\\ y\\ z\end{matrix}\right].$ (3) $$

Applying a small 3D displacement $(\delta x,\delta y,\delta z)$, its projected 2D shift $(\delta u,\delta v)$ becomes:

$$ $\delta u=f_{x}\left(\frac{x+\delta x}{z+\delta z}-\frac{x}{z}\right),\quad\delta v=f_{y}\left(\frac{y+\delta y}{z+\delta z}-\frac{y}{z}\right),$ (4) $$

where $f_{x}$ and $f_{y}$ are the focal lengths of the camera. Since the drag operations are defined on the 2D image plane (in our task), the motion along the optical axis (i.e., the $z$-axis) can be reasonably neglected. Thus, Eq. ([4](https://arxiv.org/html/2509.25740v1#S3.E4)) can be simplified as:

$$ $\delta u=f_{x}({\delta x}/{z}),\quad\delta v=f_{y}({\delta y}/{z}).$ (5) $$

Furthermore, consider another arbitrary 3D point $(x^{\prime},y^{\prime},z^{\prime})$ which is subjected to the same displacement vector $(\delta x,\delta y,\delta z)$. We can also compute its corresponding 2D displacement $(\delta u^{\prime},\delta v^{\prime})$ as $\delta u^{\prime}=f_{x}\frac{\delta x}{z^{\prime}}$ and $\delta v^{\prime}=f_{y}\frac{\delta y}{z^{\prime}}.$
In this way, combining Eq. ([5](https://arxiv.org/html/2509.25740v1#S3.E5)) yields

$$ $\delta u^{\prime}=({z}/{z^{\prime}})\delta u,\quad\delta v^{\prime}=({z}/{z^{\prime}})\delta v.$ (6) $$

Eq. ([6](https://arxiv.org/html/2509.25740v1#S3.E6)) implies that $(u^{\prime},v^{\prime})$ with a smaller depth (closer to the camera) exhibit a greater pixel-plane displacement due to the inverse proportionality between displacement and depth. Based on this observation, the geometry-aware field can be constructed as follows:

$$ $\boldsymbol{f}_{d}=\left(\boldsymbol{\zeta}_{\boldsymbol{h}}/\boldsymbol{\zeta}\right)^{\alpha}\cdot\boldsymbol{d}=\left(\boldsymbol{\zeta}_{\boldsymbol{h}}/\boldsymbol{\zeta}\right)^{\alpha}\cdot(\boldsymbol{t}-\boldsymbol{h}),$ (7) $$

where $\boldsymbol{\zeta}$ denotes the depth map within mask, and $\boldsymbol{\zeta}_{\boldsymbol{h}}$ is the depth of handle point $\boldsymbol{h}$.
The scalar $\alpha$ serves as a modulation factor, controlling the sensitivity of displacement scaling to depth variations. $\boldsymbol{d}$ is the drag direction from handle $\boldsymbol{h}$ to target $\boldsymbol{t}$. The geometry-aware influence function (i.e., Eq. ([7](https://arxiv.org/html/2509.25740v1#S3.E7))) calculates the geometry-aware displacement field (as shown in the central blue-shaded region of Fig. [3](https://arxiv.org/html/2509.25740v1#S3.F3)) based on the underlying 3D structure. By incorporating depth-dependent modulation, GeoDrag brings 3D geometric information into 2D drag editing, enabling structure-preserving manipulations. Our strategy resolves the challenge by maintaining geometric consistency between the perceived 2D deformation and the actual 3D transformation.

### 3.2 Spatial Plane Modulation

While geometry-aware displacement field provides structural consistency by incorporating 3D depth information, it alone is insufficient for producing high-quality edits—particularly in regions with fine details or near object boundaries. This limitation arises because geometry-aware motion distributes influence uniformly in 3D space, making it less responsive to subtle and local deformations in the 2D image plane (see Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1)(b)). This is the second major challenge discussed in Sec. [1](https://arxiv.org/html/2509.25740v1#S1). To overcome this, we propose a spatial plane modulation strategy that complements the global structure-preserving behavior of the geometry-aware field with local and pixel-level controllability. This hybrid approach enables precise and sharp edits while retaining geometric coherence.

Our fusion mechanism draws inspiration from elastic force propagation: deformation peaks at the force point and decays with distance. Mimicking this behavior, we define a plane-aware field that decays spatially from the handle point. This formulation allows localized and responsive editing, especially near fine structural features. While this idea is conceptually similar to the influence decay used in FastDrag [18], our method avoids plane geometric constructions like similar triangles and instead adopts a simpler, vectorized formulation that is more computationally efficient and easier to integrate.

Figure: Figure 4: Illustration of $\boldsymbol{L}$ in the plane-aware field. $\boldsymbol{O}$ and $r$ are the center of the outer circle and radius, respectively.
Refer to caption: x4.png

Given a handle point $\boldsymbol{h}$ and its target point $\boldsymbol{t}$, the drag vector is $\boldsymbol{d}=\boldsymbol{t}-\boldsymbol{h}$. The displacement at each pixel is then computed by modulating the displacement vector $\boldsymbol{d}$ according to its spatial distance to $\boldsymbol{h}$, following the spatial influence function:

$$ $\boldsymbol{f}_{p}=\left(\boldsymbol{1}-\left({\boldsymbol{P}}/{\boldsymbol{L}}\right)^{\beta}\right)\cdot\boldsymbol{d},$ (8) $$

where $\boldsymbol{1}\in\mathbb{R}^{h\times w}$ denotes a matrix with all elements as one, $\boldsymbol{P}\in\mathbb{R}^{h\times w}$ denotes the Euclidean distance from each pixel to the handle point $\boldsymbol{h}$, $\boldsymbol{L}\in\mathbb{R}^{h\times w}$ is the maximum propagation distance along the ray from $\boldsymbol{h}$ to each pixel, and $\beta$ controls how sharply the influence falls off with distance.

The propagation is restricted within a circular region enclosing the editing mask, ensuring the influence fades smoothly near the mask boundary. As shown in Fig. [4](https://arxiv.org/html/2509.25740v1#S3.F4), to compute $\boldsymbol{L}$, we solve for the ray-circle intersection:

$$ $|\boldsymbol{h}+t\boldsymbol{v}-\boldsymbol{O}|^{2}=r^{2}\quad\Rightarrow\quad t=-\boldsymbol{v}\cdot(\boldsymbol{O}-\boldsymbol{h})+\sqrt{(\boldsymbol{v}\cdot(\boldsymbol{O}-\boldsymbol{h}))^{2}-(|\boldsymbol{O}-\boldsymbol{h}|^{2}-r^{2})},$ (9) $$

where $\boldsymbol{v}=\frac{\boldsymbol{q}-\boldsymbol{h}}{|\boldsymbol{q}-\boldsymbol{h}|}$ is the unit direction vector from $\boldsymbol{h}$ to pixel $\boldsymbol{q}$,
and $\boldsymbol{L}=|\boldsymbol{h}+t\boldsymbol{v}|$ gives the maximum extent of influence.

To achieve both structural consistency and local flexibility, we fuse the geometry-aware field $\boldsymbol{f}_{d}$ and the plane-aware field $\boldsymbol{f}_{p}$ into a single displacement field $\boldsymbol{f}$:

$$ $\boldsymbol{f}=(\boldsymbol{1}-\boldsymbol{\lambda})\cdot\boldsymbol{f}_{p}+\boldsymbol{\lambda}\cdot\boldsymbol{f}_{d}.$ (10) $$

Here, $\boldsymbol{\lambda}$ is a spatially adaptive fusion weight based on the distance from each pixel to handle point, formulated as $\boldsymbol{\lambda}={\boldsymbol{P}}/({\boldsymbol{P}+\gamma})$. Where $\gamma\geq 0$ is a hyperparameter controlling the balance between global geometry-aware and local plane-aware influence. A smaller $\gamma$ favors geometric consistency, while a larger $\gamma$ increases responsiveness to localized changes. As shown in the rightmost part of Fig. [3](https://arxiv.org/html/2509.25740v1#S3.F3), the fused field integrates 3D geometric priors and 2D plane cues to enable semantically coherent and structure-preserving displacements. Since the ideal fusion scale varies across different object sizes and editing regions, we define $\gamma$ as a scalar multiple of the diameter of the enclosing mask circle, making the fusion strategy adaptive to the editing context.

### 3.3 Conflict-Free Partitioning

When multiple handle-target pairs are involved in drag-based editing, directly aggregating their displacement fields can lead to destructive interference—particularly when nearby handles induce conflicting motion directions. This is the third major challenge outlined in Sec. [1](https://arxiv.org/html/2509.25740v1#S1). Such interference often results in weakened motion strength, ambiguous displacement patterns, and ultimately, failed or unintuitive edits. Naive approaches like distance-based weighting are insufficient in these scenarios since they cannot fully decouple the influence of closely spaced or competing drag handles (see Fig. [6](https://arxiv.org/html/2509.25740v1#S4.F6)). To resolve this, we introduce a conflict-free partitioning that enforces local independence by spatially partitioning the editing mask into multiple sub-regions. Each sub-region is exclusively influenced by a single handle point, ensuring that conflicting displacements are isolated and handled separately. This strategy significantly improves editing precision and prevents cross-handle interference.

Given an editing mask $\boldsymbol{M}$, we divides it into disjoint sub-regions $\boldsymbol{\mathcal{S}}_{i}$ via Eq. ([11](https://arxiv.org/html/2509.25740v1#S3.E11)), where each pixel $\boldsymbol{q}\in\boldsymbol{M}$ is assigned to the nearest handle point $\boldsymbol{h}_{i}$.

$$ $\boldsymbol{\mathcal{S}}_{i}=\left\{\boldsymbol{q}\in\boldsymbol{M}\;\middle|\;i=\arg\min\nolimits_{j\in\{1,\dots,N\}}\|\boldsymbol{q}-\boldsymbol{h}_{j}\|_{2}\right\}.$ (11) $$

This Voronoi-like partition ensures that each sub-region $\boldsymbol{\mathcal{S}}_{i}$ is controlled only by its corresponding handle point $\boldsymbol{h}_{i}$, effectively decoupling the influence zones and eliminating destructive overlap.

Once the partitioning is established, we compute the displacement field $\boldsymbol{f}_{i}$ independently for each sub-region $\boldsymbol{\mathcal{S}}_{i}$ using the hybrid geometry- and plane-aware formulation from the previous section. The final displacement field $\boldsymbol{f}$ is constructed by assigning the corresponding sub-field to each pixel:

$$ $\boldsymbol{f}(\boldsymbol{q})=\boldsymbol{f}_{i}(\boldsymbol{q}),\quad\text{for }\boldsymbol{q}\in\boldsymbol{\mathcal{S}}_{i}.$ (12) $$

This region-wise aggregation ensures that each pixel is influenced by only one handle, avoiding directional conflicts and enabling precise and localized edits—even when multiple drags are applied. Despite being a hard partition, our ablations (see Fig. [6](https://arxiv.org/html/2509.25740v1#S4.F6)) show it performs better than soft partitioning (Directly Add, Pixel Distance, and Drag Magnitude).

## 4 Experiments

Figure: Figure 5: Qualitative comparisons with the state-of-the-art interactive point-based methods. See Appendix [D](https://arxiv.org/html/2509.25740v1#A4) for extended qualitative comparisons, including additional visualizations in Fig. [18](https://arxiv.org/html/2509.25740v1#A9.F18). In addition, see Appendix [G](https://arxiv.org/html/2509.25740v1#A7) for details on how mask selection influences editing behavior. Red points mark handles, and blue points mark targets; the same applies to the following figures.
Refer to caption: x5.png

**Table 1: Quantitative results on DragBench. Lower MD and DAI indicate higher editing precision, and higher IF reflects greater similarity between original and edited images. Time is the average editing time per point, and Mem is the peak GPU memory (GB).**
| Approach | MD $\downarrow$ | DAI1 $\downarrow$ | DAI10 $\downarrow$ | DAI20 $\downarrow$ | IF $\uparrow$ | Preparation | Time (s) | Mem |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| DragDiffusion [3] | 34.57 | 0.181 | 0.170 | 0.160 | 0.871 | $\sim$1 min (LoRA) | 22.46 | 18.63 |
| FreeDrag [13] | 30.80 | 0.183 | 0.166 | 0.151 | 0.845 | $\sim$1 min (LoRA) | 42.90 | 18.90 |
| CLIPDrag [32] | 34.62 | 0.195 | 0.174 | 0.158 | 0.891 | $\sim$1 min (LoRA) | 38.21 | 22.72 |
| AdaptiveDrag [16] | 32.38 | 0.180 | 0.154 | 0.146 | 0.830 | $\sim$1 min (LoRA) | 46.30 | 7.71 |
| DragNoise [12] | 33.84 | 0.179 | 0.169 | 0.158 | 0.861 | $\sim$1 min (LoRA) | 21.12 | 18.36 |
| FastDrag [18] | 32.10 | 0.131 | 0.123 | 0.115 | 0.850 | ✗ | 3.23 | 5.85 |
| GeoDrag (Ours) | 29.24 | 0.128 | 0.120 | 0.111 | 0.847 | ✗ | 3.95 | 5.44 |

### 4.1 Qualitative Evaluation

We conduct qualitative comparisons against existing state-of-the-art drag-based image editing methods, including DragDiffusion [3], DragNoise [12], FreeDrag [13], and FastDrag [18]. As shown in Fig. [5](https://arxiv.org/html/2509.25740v1#S4.F5), GeoDrag achieves superior performance and high image quality. For instance, in the first row of Fig. [5](https://arxiv.org/html/2509.25740v1#S4.F5), GeoDrag accurately drags the handle points toward the target points, preserving both structural integrity and semantic coherence, while other methods, such as FastDrag and FreeDrag, fail to maintain precise alignment. In multi-point editing (e.g., the second, fourth, and fifth rows of Fig. [5](https://arxiv.org/html/2509.25740v1#S4.F5)), GeoDrag successfully reshapes the wings, adjusts postures in alignment with the user-specified editing intention. In contrast, due to conflicts among multiple drag points, other methods struggle to generate coherent deformations. Observation from the last three rows of Fig. [5](https://arxiv.org/html/2509.25740v1#S4.F5), GeoDrag produces 3D structure-coherent manipulation. These advantages are derived from the integration of geometric information, which provides a displacement field toward 3D structure alignment, enabling structurally consistent editing.

### 4.2 Quantitative evaluation

Figure: Figure 6: Ablation study on multi-point drag strategies. See quantitative results in Appendix [C.1](https://arxiv.org/html/2509.25740v1#A3.SS1).
Refer to caption: x6.png

Figure: Figure 7: User study ranking on editing quality.
Refer to caption: x7.png

Figure: Figure 9: Hyperparameter sensitivity study. Left: Visual comparisons under different perceptual region $\gamma$. Right: Quantitative comparisons with varying modulation factors $\alpha$ and $\beta$. See more results in Appendix [C.2](https://arxiv.org/html/2509.25740v1#A3.SS2) and Appendix [C.3](https://arxiv.org/html/2509.25740v1#A3.SS3).
Refer to caption: x9.png

Here we conduct quantitative evaluations to validate GeoDrag where its modulation factors $\alpha$, $\beta$, and $\gamma$ are set to $1.0$. Apart from [3, 12, 13, 18], CLIPDrag [32] and AdaptiveDrag [16] are included for comparison. DragBench dataset [3] is used as the benchmark, while Mean Distance (MD) [11] and Image Fidelity (IF) [5] are metrics for evaluating the editing precision and similarity between edited and original images. Dragging Accuracy Index (DAI) [15] measures consistency in the dragged region, with DAIr evaluating a radius-$r$ patch. We also report average editing time per point and peak GPU memory.

As reported in Table [1](https://arxiv.org/html/2509.25740v1#S4.T1), GeoDrag achieves the best editing precision with the lowest MD and DAI, while maintaining competitive perceptual quality reflected by IF metric. Despite not requiring any preparation overhead, such as LoRA tuning, GeoDrag outperforms all baselines. GeoDrag edits each point in 3.95 seconds on average—faster than most diffusion-based methods—and consumes little GPU memory, making it suitable for responsive applications.
More results on scalability w.r.t. the number of drag points are in Appendix [F](https://arxiv.org/html/2509.25740v1#A6).
We also conduct a user study using 10 randomly selected images, each edited by FreeDrag [13], FastDrag [18], and our GeoDrag. 60 Participants are asked to rank the edited results (1 for best, 3 for worst). As shown in Fig. [7](https://arxiv.org/html/2509.25740v1#S4.F7), GeoDrag is superior to other methods.

### 4.3 Ablation Study

Displacement Field. We conduct ablation studies to investigate the contribution of each component in our hybrid displacement field. Specifically, w/o Depth removes the depth-aware field, while w/o Plane removes the plane-aware field. As shown in Fig. [8](https://arxiv.org/html/2509.25740v1#S4.F8), removing the depth-aware field leads to inaccurate editing (e.g., failure to rotate the car). Removing plane-aware field leads to insufficient editing. The results highlight the complementary roles of 3D geometry and 2D plane prior in achieving structure-preserving and semantically coherent editing.

Conflict-Free Partitioning. We evaluate the proposed conflict-free partitioning strategy with direct summation (Directly Add), pixel-distance weighting (Pixel Distance), and drag-magnitude weighting (Drag Magnitude). As shown in Fig. [6](https://arxiv.org/html/2509.25740v1#S4.F6), directly adding displacement fields leads to conflict and cancellation when directions oppose; Pixel Distance and Drag Magnitude cannot effectively separate influence regions, producing duplicated and unsatisfactory results; Our method avoids interference among multiple drag points, yielding accurate results.

Hyperparameters. We visually analyze the influence of $\gamma$. As shown in Fig. [9](https://arxiv.org/html/2509.25740v1#S4.F9)(left), setting $\gamma$ in the range of 0.5 to 1.5 achieves a good balance between geometry-aware consistency and local editability. We analyze the impact of $\alpha$ and $\beta$ in Fig. [9](https://arxiv.org/html/2509.25740v1#S4.F9)(right). The lower $\alpha$ indicates a smoother scale (see Eq. ([7](https://arxiv.org/html/2509.25740v1#S3.E7))), weakening the influence of depth contrast. This results in larger overall deformation and improved alignment. Larger $\alpha$ increases depth sensitivity, causing sharper displacement changes. This allows for finer-grained control in regions with significant depth changes. For plane-aware field, a higher $\beta$ enforces more localized and sharper deformations (see Eq. ([8](https://arxiv.org/html/2509.25740v1#S3.E8))), thereby better aligning the edits with user intention and resulting in lower MD. Additional ablation results on the noise-scaling term $\sigma_{t}$ in Eq. [2](https://arxiv.org/html/2509.25740v1#S3.E2) are provided in Appendix [C.5](https://arxiv.org/html/2509.25740v1#A3.SS5).

## 5 Conclusion

In this paper, we propose GeoDrag, a novel interactive editing framework that integrates 3D geometric priors with 2D spatial cues. GeoDrag achieves geometry-consistent and semantically coherent image manipulation by constructing a hybrid displacement field. A geometry-aware influence function leverages depth to model 3D-consistent displacements, while a complementary plane-aware function improves the controllability of editing. To resolve multi-point conflicts, a region-aware decomposition strategy ensures conflict-free aggregation. This work offers a new perspective on how 3D geometric priors can be beneficial for precision, coherence, and controllability of 2D interactive image editing.

Limitations. Although GeoDrag supports one-step editing, computing multiple displacement fields introduces additional computational overhead compared to lightweight 2D-only baselines such as FastDrag [18]. But GeoDrag often yields much more geometry-consistent and high-quality image edits, e.g., $9\%$ and $7\%$ improvements in terms of MD and GPU memory than FastDrag as shown in Table [1](https://arxiv.org/html/2509.25740v1#S4.T1).

## References

- [1]
Hansam Cho, Jonghyun Lee, Seoung Bum Kim, Tae-Hyun Oh, and Yonghyun Jeong.
Noise map guidance: Inversion with spatial context for real image editing.
In The Twelfth International Conference on Learning Representations, ICLR, 2024.
- [2]
Ron Mokady, Amir Hertz, Kfir Aberman, Yael Pritch, and Daniel Cohen-Or.
Null-text inversion for editing real images using guided diffusion models.
arXiv preprint arXiv:2211.09794, 2022.
- [3]
Yujun Shi, Chuhui Xue, Jun Hao Liew, Jiachun Pan, Hanshu Yan, Wenqing Zhang, Vincent Y. F. Tan, and Song Bai.
Dragdiffusion: Harnessing diffusion models for interactive point-based image editing.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 8839–8849, 2024.
- [4]
Amir Hertz, Ron Mokady, Jay Tenenbaum, Kfir Aberman, Yael Pritch, and Daniel Cohen-Or.
Prompt-to-prompt image editing with cross attention control.
arXiv preprint arXiv:2208.01626, 2022.
- [5]
Bahjat Kawar, Shiran Zada, Oran Lang, Omer Tov, Huiwen Chang, Tali Dekel, Inbar Mosseri, and Michal Irani.
Imagic: Text-based real image editing with diffusion models.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 6007–6017, 2023.
- [6]
Ling Yang, Zhaochen Yu, Chenlin Meng, Minkai Xu, Stefano Ermon, and Bin Cui.
Mastering text-to-image diffusion: Recaptioning, planning, and generating with multimodal llms.
In Forty-first International Conference on Machine Learning, ICML, 2024.
- [7]
Jun Zhou, Jiahao Li, Zunnan Xu, Hanhui Li, Yiji Cheng, Fa-Ting Hong, Qin Lin, Qinglin Lu, and Xiaodan Liang.
Fireedit: Fine-grained instruction-based image editing via region-aware vision language model.
arXiv preprint arXiv:2503.19839, 2025.
- [8]
Nataniel Ruiz, Yuanzhen Li, Varun Jampani, Yael Pritch, Michael Rubinstein, and Kfir Aberman.
Dreambooth: Fine tuning text-to-image diffusion models for subject-driven generation.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 22500–22510, 2023.
- [9]
Inbar Huberman-Spiegelglas, Vladimir Kulikov, and Tomer Michaeli.
An edit friendly DDPM noise space: Inversion and manipulations.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 12469–12478, 2024.
- [10]
Trong-Tung Nguyen, Quang Nguyen, Khoi Nguyen, Anh Tran, and Cuong Pham.
Swiftedit: Lightning fast text-guided image editing via one-step diffusion.
arXiv preprint arXiv:2412.04301, 2024.
- [11]
Xingang Pan, Ayush Tewari, Thomas Leimkühler, Lingjie Liu, Abhimitra Meka, and Christian Theobalt.
Drag your GAN: interactive point-based manipulation on the generative image manifold.
In ACM SIGGRAPH 2023 Conference Proceedings, SIGGRAPH, pages 78:1–78:11, 2023.
- [12]
Haofeng Liu, Chenshu Xu, Yifei Yang, Lihua Zeng, and Shengfeng He.
Drag your noise: Interactive point-based editing via diffusion semantic propagation.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 6743–6752, 2024.
- [13]
Pengyang Ling, Lin Chen, Pan Zhang, Huaian Chen, Yi Jin, and Jinjin Zheng.
Freedrag: Feature dragging for reliable point-based image editing.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 6860–6870, 2024.
- [14]
Xingzhong Hou, Boxiao Liu, Yi Zhang, Jihao Liu, Yu Liu, and Haihang You.
Easydrag: Efficient point-based manipulation on diffusion models.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 8404–8413, 2024.
- [15]
Zewei Zhang, Huan Liu, Jun Chen, and Xiangyu Xu.
Gooddrag: Towards good practices for drag editing with diffusion models.
In The Thirteenth International Conference on Learning Representations, ICLR, 2025.
- [16]
DuoSheng Chen, Binghui Chen, Yifeng Geng, and Liefeng Bo.
Adaptivedrag: Semantic-driven dragging on diffusion-based image editing.
arXiv preprint arXiv:2410.12696, 2024.
- [17]
Joonghyuk Shin, Daehyeon Choi, and Jaesik Park.
Instantdrag: Improving interactivity in drag-based image editing.
In SIGGRAPH Asia 2024 Conference Papers, SA, pages 39:1–39:10, 2024.
- [18]
Xuanjia Zhao, Jian Guan, Congyi Fan, Dongli Xu, Youtian Lin, Haiwei Pan, and Pengming Feng.
Fastdrag: Manipulate anything in one step.
In Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurIPS, 2024.
- [19]
Jingyi Lu, Xinghui Li, and Kai Han.
Regiondrag: Fast region-based image editing with diffusion models.
In The 18th European Conference on Computer Vision, ECCV, pages 231–246, 2024.
- [20]
Simian Luo, Yiqin Tan, Longbo Huang, Jian Li, and Hang Zhao.
Latent consistency models: Synthesizing high-resolution images with few-step inference.
arXiv preprint arXiv:2310.04378, 2023.
- [21]
Rinon Gal, Yuval Alaluf, Yuval Atzmon, Or Patashnik, Amit Haim Bermano, Gal Chechik, and Daniel Cohen-Or.
An image is worth one word: Personalizing text-to-image generation using textual inversion.
In The Eleventh International Conference on Learning Representations, ICLR, 2023.
- [22]
Gwanghyun Kim, Taesung Kwon, and Jong Chul Ye.
Diffusionclip: Text-guided diffusion models for robust image manipulation.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 2416–2425, 2022.
- [23]
Chen Henry Wu and Fernando De la Torre.
A latent space of stochastic diffusion models for zero-shot image editing and guidance.
In IEEE/CVF International Conference on Computer Vision, ICCV, pages 7344–7353, 2023.
- [24]
Tim Brooks, Aleksander Holynski, and Alexei A. Efros.
Instructpix2pix: Learning to follow image editing instructions.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 18392–18402, 2023.
- [25]
Jonathan Ho, Ajay Jain, and Pieter Abbeel.
Denoising diffusion probabilistic models.
In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS, 2020.
- [26]
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer.
High-resolution image synthesis with latent diffusion models.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 10674–10685, 2022.
- [27]
Yutao Cui, Xiaotong Zhao, Guozhen Zhang, Shengming Cao, Kai Ma, and Limin Wang.
Stabledrag: Stable dragging for point-based image editing.
In The 18th European Conference on Computer Vision, ECCV, pages 340–356, 2024.
- [28]
Shen Nie, Hanzhong Allan Guo, Cheng Lu, Yuhao Zhou, Chenyu Zheng, and Chongxuan Li.
The blessing of randomness: SDE beats ODE in general diffusion-based image editing.
In The Twelfth International Conference on Learning Representations, ICLR, 2024.
- [29]
Chong Mou, Xintao Wang, Jiechong Song, Ying Shan, and Jian Zhang.
Dragondiffusion: Enabling drag-style manipulation on diffusion models.
In The Twelfth International Conference on Learning Representations, ICLR, 2024.
- [30]
Chong Mou, Xintao Wang, Jiechong Song, Ying Shan, and Jian Zhang.
Diffeditor: Boosting accuracy and flexibility on diffusion-based image editing.
In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 8488–8497, 2024.
- [31]
Gwanhyeong Koo, Sunjae Yoon, Younghwan Lee, Ji Woo Hong, and Chang D. Yoo.
Flowdrag: 3d-aware drag-based image editing with mesh-guided deformation vector flow fields.
arXiv preprint arXiv:2507.08285, 2025.
- [32]
Ziqi Jiang, Zhen Wang, and Long Chen.
Combining text-based and drag-based editing for precise and flexible image editing.
arXiv preprint arXiv:2410.03097, 2024.
- [33]
Lihe Yang, Bingyi Kang, Zilong Huang, Zhen Zhao, Xiaogang Xu, Jiashi Feng, and Hengshuang Zhao.
Depth anything V2.
In Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurIPS, 2024.
- [34]
Edward J. Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen.
Lora: Low-rank adaptation of large language models.
In The Tenth International Conference on Learning Representations, ICLR, 2022.

## Appendix A Broader Impact

GeoDrag is developed to improve the controllability and fidelity of interactive point-based image editing, enabling precise user-driven visual manipulation. The framework applies to a wide range of scenarios, including digital content creation, artistic editing, and AR/VR-based scene editing. By improving the structural consistency and semantic fidelity, GeoDrag allows users—especially non-experts—to produce high-quality and visually coherent results with minimal effort, potentially democratizing advanced visual editing workflows. However, the increased realism and control enabled by GeoDrag may raise negative societal impacts. In particular, malicious actors could leverage the system to generate visually convincing but deceptive content, contributing to disinformation, digital impersonation, or reputational harm. In addition, advancements in image editing tools increase the risk of fake imagery, potentially undermining public trust. Unethical use may also raise concerns related to individual consent and personal privacy. To address these risks, we advocate for responsible deployment, transparent provenance of generated content, and further research into detection and authentication techniques.

## Appendix B Implementation Details

GeoDrag is implemented based on a pretrained latent diffusion model (Stable Diffusion 1.5 [26]), and incorporates an LCM-accelerated U-Net [20] to enable efficient low-step inference. We set the number of sampling steps to 10 and use an inversion strength of $0.7$. The depth prediction model used in geometry-aware field modeling (Sec. [3.1](https://arxiv.org/html/2509.25740v1#S3.SS1)) is Depth Anything V2 [33]. Following prior drag-based editing methods [3, 13, 12], we disable classifier-free guidance. For fair comparison, all baseline methods are evaluated using their default hyperparameter settings as specified in the original papers or official open-source implementations. Experiments are conducted on an RTX 4090 GPU with 24G memory.

## Appendix C Supplementary Ablation Study

### C.1 Quantitative Ablations on Displacement Field and Multi-Point Dragging

Figure: (a) Displacement field variants (cf. Fig. [8](https://arxiv.org/html/2509.25740v1#S4.F8)).
Refer to caption: x10.png

We present additional quantitative results to validate the effectiveness of our hybrid displacement field and conflict-free partitioning strategy. As shown in Fig. [10](https://arxiv.org/html/2509.25740v1#A3.F10)(a), GeoDrag with geometry- and plane-aware displacement field achieves the best performance. Removing the geometry prior (w/o Depth) or the plane modulation (w/o Plane) leads to degradation across all metrics.

The quantitative results of different multi-point dragging strategies are shown in Fig. [10](https://arxiv.org/html/2509.25740v1#A3.F10)(b). GeoDrag outperforms alternative strategies on all metrics, demonstrating the effectiveness of the conflict-free partitioning. The mathematical formulations of alternative strategies are provided below:

$$ Directly Add: $\displaystyle\boldsymbol{f}=\sum_{i=1}^{k}\boldsymbol{f}_{i},$ (13) Pixel Distance: $\displaystyle\boldsymbol{f}=\sum_{i=1}^{k}\frac{1/\boldsymbol{P}_{i}}{\sum_{i=1}^{k}1/\boldsymbol{P}_{i}}\boldsymbol{f}_{i},$ (14) Drag Magnitude: $\displaystyle\boldsymbol{f}=\sum_{i=1}^{k}\frac{|d_{i}|}{\sum_{i=1}^{k}|d_{i}|}\boldsymbol{f}_{i},$ (15) $$

where $\boldsymbol{P}_{i}$ is the pixel-wise distance map to handle point $h_{i}$, and $|d_{i}|$ denotes the drag magnitude of $h_{i}$.

### C.2 Visual results of modulation factors

Moreover, we present the visual results of different combinations of $\alpha$ and $\beta$ in Fig. [17](https://arxiv.org/html/2509.25740v1#A9.F17). It is evident that GeoDrag well aligns with user-specified drag points, demonstrating its robustness across parameter variations. We observe that increasing $\alpha$ enhances the influence of geometric guidance during editing. As illustrated in the fourth row of Fig. [17](https://arxiv.org/html/2509.25740v1#A9.F17), when $\alpha=2$, the result exhibits a more plausible 3D transformation: the mushroom cap appears lifted along a realistic vertical trajectory, consistent with a bottom-up viewpoint. This demonstrates the role of geometric priors in maintaining a consistent 3D perspective during editing.

### C.3 Quantitative results of different γ \gamma

The quantitative results of different perceptual region $\gamma$ are presented in Fig. [13](https://arxiv.org/html/2509.25740v1#A3.F13). As $\gamma$ increases, MD consistently decreases, while IF exhibits a non-monotonic trend—first increasing, then decreasing. Notably, $\gamma=1$ offers a favorable balance between editing accuracy and image fidelity, and is thus selected as the default setting in our experiments.

### C.4 Ablation study on inversion steps

We experiment with $t\in\{4,7,10,13,20,35,50\}$ to examine the number of inversion steps in diffusion inversion. The qualitative and quantitative results are given in Fig. [13](https://arxiv.org/html/2509.25740v1#A3.F13) and Fig. [13](https://arxiv.org/html/2509.25740v1#A3.F13), respectively. We observe that GeoDrag achieves more precise and faithful edits when the number of inversion steps $t\leq 10$.

Figure: Figure 11: Ablation study on $\gamma$ in terms of quantitative metrics.
Refer to caption: x12.png

Figure: Figure 14: Ablation study on the noise-scaling term $\sigma_{t}$ controlled by $\eta$. We vary $\eta$ from 0 (deterministic) to $1$ (stochastic).
Refer to caption: x15.png

In contrast, when $t>10$, the editing quality degrades. For a fair comparison with FastDrag [18], and to balance editing performance with fidelity to the original image, we adopt 10 as the default setting for inversion steps throughout all experiments in the paper.

Figure: (a) Color wheel used for displacement field visualization.
Refer to caption: figures/flow_legend.png

### C.5 Ablation on the Noise-Scaling Term σ t \sigma_{t}

We conduct an ablation study on the noise-scaling term $\sigma_{t}$ in Eq. ([2](https://arxiv.org/html/2509.25740v1#S3.E2)), which is controlled by the stochasticity parameter $\eta$:

$$ $\sigma_{t}=\eta\cdot\sqrt{\frac{1-\bar{\alpha}_{t-1}}{1-\bar{\alpha}_{t}}}\cdot\sqrt{1-\frac{\bar{\alpha}_{t}}{\bar{\alpha}_{t-1}}}.$ (16) $$

Recall that $\sigma_{t}$ sets the magnitude of the random noise injected by the masked stochastic DDIM step (Eq. [2](https://arxiv.org/html/2509.25740v1#S3.E2)). As shown in Fig. [14](https://arxiv.org/html/2509.25740v1#A3.F14), setting $\eta=0$ leads to a fully deterministic update, which often produces over-smoothed results after interpolation and thus blurs in the background. Increasing $\eta$ injects stronger randomness inside the interpolated region, encouraging the diffusion model to better infer local details there. These results highlight the importance of controlled noise injection: moderate stochasticity yields sharper and more faithful refinements without incurring additional sampling overhead.

## Appendix D More Visualization Comparison

We present additional qualitative comparisons between our method and other state-of-the-art interactive point-based editing methods. As shown in Fig. [18](https://arxiv.org/html/2509.25740v1#A9.F18), these results further demonstrate the advantages of GeoDrag across various scenarios, including rotation (e.g., dog, car), scale manipulation (e.g., the avocado and burger), stretching (e.g., the bench), and geometry-consistent movement (e.g., the mailbox and car). Compared to other methods, GeoDrag better preserves object structure while producing edits that better conform to the user input. In challenging cases involving perspective shifts (e.g., the last row), GeoDrag generates geometry-consistent results that maintain alignment with the user-specified drag. These results demonstrate GeoDrag’s ability to preserve visual coherence under complex editing operations.

## Appendix E Effect of LoRA Finetuning on GeoDrag

**Table 2: Quantitative comparison of GeoDrag with and without LoRA finetuning.**
| Method | MD $\downarrow$ | DAI1 $\downarrow$ | DAI10 $\downarrow$ | DAI20 $\downarrow$ | IF $\uparrow$ |
| --- | --- | --- | --- | --- | --- |
| w/o LoRA | $29.24$ | $0.128$ | $0.120$ | $0.111$ | $0.848$ |
| w/ LoRA | $30.91$ | $0.186$ | $0.163$ | $0.146$ | $0.851$ |

To further investigate the generalization ability of GeoDrag, we evaluate GeoDrag under two configurations: with and without LoRA [34] finetuning. Both versions share the same backbone and inference hyperparameters; the only difference is whether LoRA finetuning is applied. As shown in visual examples (see Fig. [19](https://arxiv.org/html/2509.25740v1#A9.F19)), GeoDrag consistently produces high-quality, geometry-consistent edits even without any finetuning. Nevertheless, LoRA finetuning can enhance local detail and fidelity in some cases (e.g., the fourth row of Fig. [19](https://arxiv.org/html/2509.25740v1#A9.F19)).

The quantitative results are reported in Table [2](https://arxiv.org/html/2509.25740v1#A5.T2). The model without LoRA achieves lower MD and DAI, indicating better alignment with editing guidance. Meanwhile, LoRA finetuning improves visual similarity between the original and edited images (higher IF).

## Appendix F Scalability with the number of drag points

To evaluate scalability as the number of drag points increases, we conduct a dedicated experiment: 10 representative images are selected and applied 1–8 drag points, yielding a total of 80 edited samples. We measured the average per-image editing time for each point count. As reported in Table [3](https://arxiv.org/html/2509.25740v1#A6.T3), the number of drag points has minimal impact on editing time, supporting the practicality of GeoDrag for interactive workflows.

**Table 3: Average editing time (in seconds) for different numbers of drag points.**
| Number of points | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Time (seconds) | $12.71s$ | $11.63s$ | $11.74s$ | $11.23s$ | $12.27s$ | $12.86s$ | $12.03s$ | $12.93s$ |

## Appendix G Effect of Masks

Figure: (a) Full-object mask (global edit).
Refer to caption: x16.png

Mask selection is crucial for controlling the scope and locality of edits. Figure [16](https://arxiv.org/html/2509.25740v1#A7.F16) illustrates the impact of different masks when edit a same object. Applying a full-object mask to the avocado enlarges the entire object (Figure [16](https://arxiv.org/html/2509.25740v1#A7.F16)(a)) and the shape of the seed is changed. In contrast, masking only the avocado’s edges confines the effect to the boundary (Figure [16](https://arxiv.org/html/2509.25740v1#A7.F16)(b)), preserving the shape of seed.

## Appendix H Visualization of Displacement Fields

To provide a better understanding of how user-specified drags are propagated, we visualize the 2D displacement fields (see Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1) and Fig. [3](https://arxiv.org/html/2509.25740v1#S3.F3)). These displacement fields are color-coded using a consistent scheme to indicate direction and magnitude, as shown in Fig. [15](https://arxiv.org/html/2509.25740v1#A3.F15)(a). Hue represents the direction of displacement, with each color corresponding to a specific motion orientation (e.g., rightward in red, upward in cyan). Brighter and more saturated regions correspond to larger displacement magnitudes.

In addition, Fig. [15](https://arxiv.org/html/2509.25740v1#A3.F15)(b) shows the legend used for visualizing depth or distance maps. Warmer colors indicate closer regions and cooler colors denote farther ones. This legend is used in visualizations such as depth and distance maps in Fig. [1](https://arxiv.org/html/2509.25740v1#S1.F1).

## Appendix I Details of User Study

Here, we provide additional details about the user study, including its design and aggregated ranking-based evaluation results. Fig. [20](https://arxiv.org/html/2509.25740v1#A9.F20) shows the selected input images, the corresponding editing results from different methods, and the user-assigned rankings for each result. For each test case, users were asked to rank the edited results from three different methods. The ranking is based on how well each result aligns with the intended dragging operation while preserving the original visual identity. A lower rank indicates better quality. Specifically, rank 1 denotes the best edit—i.e., the one that best aligns with the drag intention and maintains high image fidelity—while rank 3 corresponds to the least satisfactory result. Note that the anonymous labels (a), (b), and (c) correspond to FastDrag [18], FreeDrag [13], and GeoDrag, respectively.

Figure: Figure 17: Visual Results of Hyperparameter Analysis.
Refer to caption: x18.png

Figure: Figure 18: More qualitative comparisons with state-of-the-art interactive point-based methods.
Refer to caption: x19.png

Figure: Figure 19: Visual comparison of GeoDrag with and without LoRA [34] finetuning. w/ LoRA and w/o LoRA denote our GeoDrag with and without finetuning, respectively.
Refer to caption: x20.png

Figure: Figure 20: Examples and detailed user rankings for the user study. For each case, we show the original image, the user input, and editing results from three anonymous methods labeled as (a), (b), and (c). The number of Rank-1, Rank-2, and Rank-3 votes collected from all participants is reported. A lower rank indicates better alignment with the intended manipulation and higher visual fidelity.
Refer to caption: x21.png

## Peer Reviews

confidence: 3
contribution: 3
initial_rating: 6
presentation: 3
questions: * In practice, one common idea is that LoRA should improve the performance in drag editing. However, Table 2 suggests that LoRA actually hurts the performance for most metrics. Is there any further explanation or examples?
soundness: 3
strengths: * The derivation from 3D displacement to 2D motion motivates a depth-modulated field that is simple, interpretable, and implementation-light. The proposed approach effectively reduces perspective-induced tearing during large drags.
* On DragBench, GeoDrag attains best MD and best DAI1/10/20 with a one-step pipeline and 3.95s per point / 5.44 GB peak memory, competitive with FastDrag’s 3.23s / 5.85 GB and faster than LoRA-prep methods (∼1-min prep). Compared with baselines, for which LoRA-prep is often necessary, the proposed method shows better generalizability.
* The partitioning successfully creates predictable, non-interfering edits. Ablations show it outperforms soft blends like Directly-Add, Pixel-Distance, and Drag-Magnitude across MD/DAI/IF (Fig. 10b)
summary: This paper proposes GeoDrag, a drag-based image editor that injects 3D geometry into 2D dragging. The authors derive a geometry-aware influence field. Specifically, per-pixel motion scales with the relative depth to a handle point, so nearer pixels move more than farther ones, reducing perspective artifacts during editing. For multi-handle cases, they introduce a conflict-free hard partition so each pixel is driven by exactly one handle, avoiding direction cancellation. On DragBench, GeoDrag achieves the best edit precision (lowest MD/DAI) with competitive speed/memory.
weaknesses: * The simplification that neglects motion along the optical axis to obtain is reasonable for small motions, but the paper does not quantify robustness to depth noise (from monocular estimation), likely failure modes for strong perspective or specular/textureless regions. A perturbation study of these factors would better support claims of geometric stability. Additional failure cases will also help to understand the limitations of the work.
* The runtime table shows FastDrag is still faster per point (3.23 s) than GeoDrag (3.95 s) on the same GPU, and the manuscript does not provide a full stack breakdown (depth inference, partitioning, field fusion, masked DDIM) to explain where time goes or how to optimize it. A consolidated per-stage timing would strengthen the efficiency story.
* Although the proposed method is claimed to work better for long-range drag operation, the qualitative results show that it still has problems where the handle points are not actually moved to the target points (Figure 5 Ours, there are always small distances). However, such a case is usually not seen in copy-paste methods like SDEDrag. 
* The geometry-aware influence field is derived under small-motion, locally smooth assumptions and works best when pixels “move with” nearby handles. However, edits that require self-occlusion swaps or reveal previously unseen regions may lead to problems.

---

confidence: 4
contribution: 2
initial_rating: 6
presentation: 3
questions: As mentioned above, in Eq. (10), λ is defined as P / (P + γ), which does not incorporate depth. Have the authors considered using a joint distance–depth weighting function to better reflect 3D spatial relationships?
soundness: 3
strengths: - GeoDrag achieves the best performance on DragBench, showing the lowest MD and DAI metrics while maintaining competitive image fidelity and efficiency.
- The framework is simple yet effective, enabling drag-based editing in a single forward pass without LoRA tuning, similar to FastDrag but extended with geometry awareness.
- By introducing geometry-aware field modeling and spatial plane modulation, the method is able to integrate 3D geometric cues into 2D editing, improving structure preservation and local controllability.
- The proposed conflict-free partitioning strategy effectively handles multi-point editing, preventing interference between overlapping drags and ensuring stable, coherent results.
summary: This paper proposes GeoDrag, a geometry-guided drag-based image editing method. Similar to FastDrag, it enables drag-based manipulation without LoRA and operates in a single forward pass. The key idea is to incorporate 3D geometric cues into 2D drag editing through geometry-aware field modeling, where displacement strength is modulated based on the depth map. In addition, the authors introduce spatial plane modulation to complement this, since geometry-aware motion distributes influence uniformly in 3D space, making it less sensitive to local details. The fusion of geometry and plane-aware fields allows the method to maintain both global structure and fine-grained local control (conceptually related to warpage vector modeling in FastDrag). Experiments on DragBench demonstrate that GeoDrag achieves lower Mean Distance (MD) and Dragging Accuracy Index (DAI) than previous state-of-the-art methods, while performing editing faster and without additional training overhead.
weaknesses: - In Section 3.2, the paper mentions that the geometry-aware displacement field “distributes influence uniformly in 3D space, making it less responsive to subtle and local deformations in 2D image plane.” However, this concept is not intuitive; additional explanation or visual illustration would help readers understand it better.
- The method heavily relies on accurate depth maps. In scenes where the depth estimation is noisy, such as generated images or complex high-frequency scenes with multiple overlapping objects, the geometry-aware field may be incorrectly computed, potentially degrading results compared to purely 2D approaches. Failure case analysis would strengthen the paper.
- Simply projecting 3D depth information into 2D space may not fundamentally resolve geometric ambiguity, since projection inherently loses spatial consistency across varying viewpoints.
- The novelty of the plane-aware field in Section 3.2 feels somewhat limited. Its formulation resembles the displacement weighting in FastDrag, which also applies a distance-based decay for local control. The paper would benefit from a clearer analysis or ablation demonstrating how the proposed plane-aware formulation improves upon or differs from *FastDrag* in practice.
- In Eq. (10), the geometry-aware and plane-aware fields are linearly interpolated with λ = P / (P + γ). This λ depends only on 2D distance and ignores depth variation, thus disconnecting from the true 3D structure. It would be interesting to see whether defining λ as a combined function of both distance and depth difference could yield a more geometrically consistent fusion.
- Missing comparison with GoodDrag (ICLR 2025), a recent baseline for drag-based editing.

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confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: 1.  Concurrent work like `Inpaint4Drag` uses inpainting to handle occlusions, which can sometimes cause warping distortions. Have the authors considered combining GeoDrag's superior geometry-aware displacement with a dedicated inpainting model? This synergy could potentially yield more realistic results at object boundaries by better handling disoccluded regions.
soundness: 3
strengths: 1.  **Novelty and Rationale:** The core strength is the novel integration of 3D geometry into the 2D drag-editing task. This is a well-motivated and logical advancement for the field, directly addressing a key limitation of prior work and yielding significant improvements in structural preservation.

2.  **Clear and Effective Framework:** The paper effectively decomposes the problem into distinct sub-challenges and proposes clear, corresponding solutions (geometry-aware field, spatial modulation, and conflict-free partitioning). This systematic approach enhances the method's robustness and clarity.

3.  **Efficiency for Interactivity:** By avoiding iterative optimization, the one-step editing process makes GeoDrag a practical and competitive solution for real-world interactive applications.
summary: This paper presents GeoDrag, a novel method for point-based image editing that addresses the limitations of 2D-only approaches in geometry-intensive scenarios. By incorporating 3D geometric cues (from a predicted depth map) into a unified displacement field, GeoDrag achieves structurally consistent edits like rotations and perspective shifts. The framework combines this geometry-aware guidance with 2D spatial priors for local detail preservation and introduces a conflict-free partitioning strategy for robust multi-point dragging, all within an efficient single-pass process.
weaknesses: 1.  **Texture and Identity Preservation:** In some cases, the edited regions exhibit a loss of texture fidelity. For instance, the "mountain" example on the project page shows the dragged peak becoming blurred, suggesting a potential trade-off between geometric deformation and preserving the original surface identity. A discussion on this limitation would be welcome.

2.  **Foreground-Background Separation:** The method can sometimes cause unnatural co-movement of the background with the dragged object. This is visible in the "duck" example, where the surrounding grass is pulled along with the head. This suggests that handling disocclusion and complex object boundaries remains an area for improvement.

3.  **Limitations of the 3D Motion Model:** The current geometric model (Eq. 7) effectively handles transformations parallel to the image plane but is a simplification of true 3D motion. This might limit its ability to perform more complex perspective changes, such as pulling an object "out of" the scene. Exploring a more comprehensive 3D motion model could be a valuable future direction.

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confidence: 2
contribution: 2
initial_rating: 4
presentation: 3
questions: 1.	How sensitive is the method to depth map errors?
2.	Can GeoDrag operate with estimated depth from monocular models?
3.	Is the diffusion model re-trained or used as a frozen backbone?
soundness: 3
strengths: 1. Addresses a concrete weakness: Most drag methods ignore geometry, causing distortions. GeoDrag effectively solves this.

2. Principled integration: The combination of 3D depth modulation and 2D plane adjustment is physically intuitive and well-designed.

3. Practical contribution: One-step editing drastically improves usability and speed over iterative gradient-based methods.

4. Strong empirical results: Quantitative improvements (1.4× DAI, 1.1× MD) and excellent qualitative visuals demonstrate real impact.

5. Multi-point conflict resolution: - The conflict-free partitioning module is a simple yet powerful idea that improves robustness.
6. Extensive evaluation: Diverse examples (faces, landscapes, multi-object scenes) show generality.
summary: GeoDrag is a geometry-aware drag-based image editing framework combining 3D structural cues and 2D spatial priors. It predicts displacement fields in diffusion latent space, incorporating depth-based modulation and spatial plane adjustment, along with a conflict-free partitioning scheme for multi-point editing.
weaknesses: 1.	Depth dependency: Accuracy hinges on reliable depth maps; the paper assumes ideal depth input without addressing noise robustness.
2.	Limited theoretical grounding: The interaction between geometry and diffusion latent space lacks mathematical explanation.
3.	Ablation insufficiency:The individual contribution of geometry-aware vs. plane-aware modules is unclear.
4..	Efficiency discussion shallow: Though claimed efficient, actual GPU/latency data is minimal.
5.	Applicability scope: Focused on still images; no experiments on video or non-diffusion backbones.
6..	Minor clarity issues: Some figures are over-compressed, making displacement fields hard to interpret.


Decision: Accept (Poster)