Positional Encoding Field
Authors: Yunpeng Bai
Haoxiang Li
Qixing Huang
Venue: ICLR 2026 Poster (2026)
Keywords: Positional Encoding
Novel View Synthesis
Geometry-Aware Generation
Image Editing
Primary area: generative models

Abstract: Diffusion Transformers (DiTs) have emerged as the dominant architecture for visual generation, powering state-of-the-art image and video models. By representing images as patch tokens with positional encodings (PEs), DiTs combine Transformer scalability with spatial and temporal inductive biases. In this work, we revisit how DiTs organize visual content and discover that patch tokens exhibit a surprising degree of independence: even when PEs are perturbed, DiTs still produce globally coherent outputs, indicating that spatial coherence is primarily governed by PEs. Motivated by this finding, we introduce the Positional Encoding Field (PE-Field), which extends positional encodings from the 2D plane to a structured 3D field. PE-Field incorporates depth-aware encodings for volumetric reasoning and hierarchical encodings for fine-grained sub-patch control, enabling DiTs to model geometry directly in 3D space. Our PE-Field–augmented DiT achieves state-of-the-art performance on single-image novel view synthesis and generalizes to controllable spatial image editing.

Published as a conference paper at ICLR 2026
POSITIONAL ENCODING FIELD
Yunpeng Bai" University of Texas Austin byp215 erp215@utexxs.eee
Haoxiang Li Pixocial Technology wiw.ann..iiiiiiiiia.a.... com
Qixing Huang
University of Texas Austin huanggxêcs ut uxax edu
ABSTRACT
Diffusion Transformers (DiTs) have emerged as the dominant architecture for vi- sual generation, powering state-of-the-art image and video models. By repre- senting images as patch tokens with positional encodings (PEs), DiTs combine Transformer scalability with spatial and temporal inductive biases. this work. we revisit how DiTs organize visual content and discover that patch tokens ex- hibit a surprising degree of independence: even when PEs are perturbed, DiT's still produce globally coherent outputs, indicating that spatial coherence is pri- marily governed by PEs. Motivated by this finding, we introduce the Positional Encoding Field (PE-Field), which extends positional encodings from the 2D plane to a structured 3D field. PE-Field incorporates depth-aware encodings for volu- metric reasoning and hierarchical encodings for fine-grained sub-patch control, enabling DiTs to model geometry directly in 3D space. Our PE-Field-augmentee DiT achieves state-of-the-ar performance single-image novel view synthesis and generalizes to controllable spatial image editing.
INTRODUCTION
Diffusion Transformers (DiTs) (Peebles & Xie 2023) have rapidly emerged as the dominant archi- tecture in visual generation, forming the backbone of recent state-of-the-arte image and video models such as Flux.1 Kontext (Labs et al. 2025), Qwwen-Image (Wu et al.) (025a), Cog Video (Yang et al.) 2024], and Wan (Wan et al. (2025). By encoding images into sequences of patch tokens and applying 2D positional encodings (PEs) Vaswani et al. 2017). DiTs leverage the scalability of Transformers while preserving the spatial inductive biases necessary for visual synthesis. This design has enabled remarkable progress, supporting high-fidelity image generation and temporally coherent video syn- thesis (where additional temporal PEs are employed).
Despite their empirical success, the internal mechanisms by which DiTs organize and compose vi- sual content remain relatively underexplored. In this work, we begin with a simple yet striking observation: patch tokens in DITs exhibit surprising degree of independence. When positional encodings are reassigned, the model still produces globally coherent output, though with patches reorganized according the altered PEs. This suggests that spatial coherence in DiTs primarily enforced by positional encodings rather than by explicit token-to- token dependencies and that ma- nipulating PEs alone can induce structured reconfiguration of spatial content. This property offers new avenue for spatially controllable generation, where images can be reorganized according to PEs transformation without modifying the token content itself.
Building this insight, we focus on single-image novel view synthesis (NVS) and extend the positional encodings of DiTs beyond the 2D image plane into a structured 3D field, which we term the Positional Encoding Field (PE-Field). The PE-Field introduces two key innovations: First, we extend standard 2D RoPE (Su et al. 2024) to a 3D depth-aware encoding, embedding tokens in volumetric field that supports reasoning across viewpoints. Second, design hierarchical scheme that subdivides tokens into finer sub- sub-patch levels, allowing different sub-vectors to capture
"This work conducted during internship Pixocial Technology.

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spatial information varying granularities. Together, these designs transform DiT' into geometry- aware generative framework that reasons directly in a 3D positional encoding field. As a result, our approach achieves state-of-the of-t----rttt-tttte results in novel view synthesis (NVS) from single image, and naturally generalizes to spatial editing tasks, where manipulating the PF-Field enables structured control of image content at both global and local levels.
Our contributions are as follows: 1) We show that DiT's can reorganize image content purely through positional encodings, revealing previously underexplored property that enables structured spatial editing. 2) We introduce depth-augmented positional encoding field that embeds tokens into a 3D space, enabling volumetric reasoning and geometric consistency. 3) We extend DiTs with multi- level positional encodings, allowing fine-grained spatial control at sub-patch granularity. 4) Our PE-Fieel augmeendd DiT' achieves state-of-the- results on novel view synthesis (NVS) from a single image, and further generalizes to spatial image editing tasks.
RELATED WORKS
2.1 NOVEL VIEW SYNTHESIS
Novel view synthesis (NVS) is a widely studied and discussed problem which can be broadly divided into two categories: methods based on multiple input images and those based on a single input image. In this work, focus the latter. The simplest approach is directly use a feed-forward model (Hong et al., 2024; Jin et al. 2025 to generate novel views from an input image. Such methods typically rely on learning intermediate, general 3D representations from data. For example, early works adopt mulli-plane representations (Zhou et al. [0188 Han et al. 2022 Tucker & Snavely) 2020), PixeINeRF (Yu YYu et al., (02T) employs NeRF (Mildenhall at 2020) as the 3D representation, LRM (Hong et al., (024) uses tri-plane representations, and 3D-GS Kerbl et al. (023) has also been adopted by methods such as PixelSplat (Charatan et al., 2024). Other methods (Wiles et al., 2020) Rombach et al., 2021; Rockwell et al. Park et al.) 2024) incorporate additional results from monocular reconstruction to provide an explicit geometric structure, where warping into the target
view is used which is then followed by inpainting synthesize novel views.
Recently, with the breakthrough of diffusion- generative models, an increasing number of works have investigated the use of diffusion models for NVS, including GeNVS (Chan al.) (023),
Zero-1-to- (Liu et al. 2023). ZeroNVS (Sargent et al.) 2024), and CAT3D (Gao et al. 2024, Wu al., 2025b). However, directly encoding camera pose conditions as text embeddings makes difficult to precisely control viewpoint changes. Reconfusion (Wu et al. 2024 uses PixeINeRF YYu al. 2021 features as diffusion conditions. but consistency across views cannot be guaranteed. The paradigm of monocular reconstruction followed by warping and inpainting has also been adopted in diffusion-based methods (Zhang et al. 2024 Chung et al., 2023, Shriram al. 2024 Yu al.,
2024 Cao et al. (2025), where diffusion is used for the inpainting stage. However, reprojection errors in the warped image may disrupt the semanties of the source image and are difficult correct during inpainting. To address this issue, GenWarp (Seo al., 2024) proposes to use warped 2D coordinates as input instead of directly warping the image, and this idea has been extended to videos in later work (Seo et al. 2025). However, since view transformation inherently occurs in 3D space, relying solely on 2D coordinates remains ambiguous, and these methods require training additional branches handle coordinate input. Many video-based models (Sun al. 2024: Huang et al., 2025 Chen et al. 2025 Ren et al. 2025) Zhhng et al., 2025 Song et al. 2025 Liang et al. (025) incorporate camera control to achieve NVS, but when only the target view is required, generating intermediate frames is unnecessary. CausNVS (Kong et al. 2025) also explores an autoregressive approach for novel view synthesis.
2.2 DITS FOR IMAGE GENERATION AND EDITING
Diffusion Transformers (DiTs) were first introduced by (Peebles & Xie 2023), who replaced the commonly used U-Net backbone in diffusion models (Rombach et al. 2022) with pure Trans- former architecture. This design leveraged the scalability and flexibility of Transformers while retaining the generative power of diffusion, and has since become the foundation of many state- of-the-art image and video generation models. Building on DiT, subsequent works such as Stable Diffusion 3 (SD3) (Esser et al. 2024), Flux.1 Kontext Laabs et al. 2025), Qwen-Image (Wu et al.
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Decode
Apply
Warp
Canonical
Warped PT
Generate
Figure I: Illustration of DiT patch-level independence. When positional encodings (PEs) of image tokens or noise tokens are reassigned, the decoded or generated outputs still produce semantically meaningful images. The resulting structures follow the positional encoding reassignment, while boundaries between patches remain visually distinct.
Reconstruction & View Transformation
Input image
Direct generation
Figure 2: Illustration of our direct novel view synthesis (NVS) Results. We apply 2D positional encodings (PEs) derived from 3D reconstruction and view transformation directly to the source-view image tokens. Using these modified tokens as image conditions in DIT enables direct generation of a relatively accurate novel-view image.
2025a), Video (Yang et al. 2024). and Wan (Wan al. 2025) have established DiT the main backbone for large-scale generative modeling. Owing to its flexible architecture, DiT can be naturally extended by incorporating the tokens of a context image directly into the input sequence, enabling end-to-end image editing within the same generative framework. This simple yet effective strategy has been widely adopted in current mainstream editing models (Labs al. 2025 Wu al.) 2025a), demonstrating the versatility of DiTs for controllable generation tasks. In contrast, pro- pose equipping DiTs with a 3D-aware hierarchical positional encoding field, enabling controllable and geometry-awen generation and editing solely through transformations positional encodings.
3 METHOD
3.1 TOKEN MANIPULATION FOR VIEW SYNTHESIS
Patch-level independence in DiT-based generative models. DiT-based architectures model image generation by patchifying the input and representing each patch a token with 2D positional encoding (PE). While tokens collectively reconstruct the image, we find that each token mainly en- codes its local patch and retains degree of independence. tokens' PEs leads to images reorganized according to the new layout, with clear patch boundaries indicating independent decoding. This independence also appears during denoising: as shown in Figure ( (Bottom), reassigning PEs of noise tokens still yiclds globally coherent results (c.g.. face) but with block-wise discontinuities aligned with the modified positions. These findings suggest that global coherence is largely enforced by PEs, enabling the possibility of spatial editing by manipu- lating token positions through their PEs without altering token content.
shown in Figure (Top), reassigning
Towards novel view synthesis via token manipulation. In this work, mainly want leverage these findings to address novel view synthesis (NVS) problem from a single image. A straight- forward solution is to perform single-view 3D reconstruction followed by view transformation and

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Illustration of hierarchical RoPE allocation in Flux (24 heads). Each rectangle on the left represents the subvector computed by one head, with colors indicating the RoPE level. Black denotes the original patch-level RoPE (I = 0), covers 256 pixels patch. Level / = corresponds to 64 pixels, and level / = 2 to 16 pixels. The square on the right represents a patch corresponding to one token, illustrating how different levels of positional encodings map to their respective 2D spatial locations, where I corresponds to 1/16-sized patch.
Figure 3:
inpainting. but this pipeline is often prone to errors (Seo et al. (024). Instead, we directly manipulate DiT's image token positions: conditioned on the source reconstruction and target camera pose, we reassign positional encodings that tokens migrate to their new projected locations. This allows composing image content under novel viewpoints within the DiT generative process, avoiding errors from direct image-space warping. As shown in Figure 2 this approach demonstrates partial but effective ability to perform NVS, but artifacts remain due to: (1) resolution mismatch-positionn grids from patch tokens (e.g., 16 16 pixels) alignment precision. The manipulation can only rearrange image content at the patch level, but it cannot alter the content within each patch. and (2) depth ambiguity-muliile 3D points may project to the same token location. Without explicit mechanisms to disambiguate depth, generated tokens can collapse into inconsistent local structures. To adapt DiTs for NVS through positional encoding transformations, we introduce two key modifications to the existing PE design, extending it into structured 3D field representation.
coarser than dense 3D reconstructions, limiting
3.2 MULTI-LEVEL POSITIONAL ENCODINGS FOR SUB- SUB-PATCH DETAIL MODELING
In the current DiT architecture, each image patch is represented as a single token, i.e., a one- dimensional vector x; Rd, which is fed into the transformer for computation. Within the trans- former, multi-head self-attention (MHA) is applied by projecting x; into multiple subspaces (heads), h E {1,.... H} with per-head dimension da (typically da d/H) enabling the model cap- ture diverse relationships across tokens. Current mainstream DiT models, such as Flux and SD3, first obtain queries, keys, and values by linear projections of the hidden states: Q XWQ. K XWK. : X WWv X B The results are then reshaped into I heads with per-head di- mension d2 = d/H: Q, K, V.V. E R
BxTxx + Bx Hx' xd., For each head, attention is computed
as head (h) = softmax RONT V(b) Finally, the outputs of all heads are concatenated and
Van
projected back to dimension d. However, all heads share the same positional encodings (specifi- cally RoPEs (Su et al. 2024)), which are tied to patch-level locations. Thus, although each token is divided across multiple heads for modeling, it still encodes the holistic content of an entire patch, without explicitly capturing finer-grained details within the patch.
We argue that this design limits the transformer's ability to capture sub-patch structures that are crucial for tasks involving fine spatial transformations such novel view synthesis. Our goal is not discard the different correspondences already learned by different heads the patch level, but rather to enrich them with intra-patcl detail modeling. To this end, we build directly the head- splitting structure of MHA, augmenting with multi-level hicrarchical positional encodings so that each head's subspace captures not only patch-level information but also finer-grained details, while remaining highly compatible with the original architecture since the finer-level PEs differ little from the original ones.
Concretely, we retain a subset of heads that use the original patch-level RoPE (l, = 0) to preserve the pretrained global structure, while other heads adopt finer-grained RoPEs derived from higher
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resolution grids (see Figure B) At level O, each positional encoding corresponds to the orig- inal patch-level RoPE (c.g., one token covers 16 x 16 pixels). When moving to higher levels, the positional grid resolution is increased: each step doubles the resolution along both axes, the effective cell size shrinks by a factor of 2 per axis (i.e., by 4 in area). Let (RoPE(l) J1, 1- de- note the hierarchy of positional encodings, where larger 4, corresponds to higher spatial resolution (doubling per axis per level). Queries and keys in head h are rotated by the level-specific RoPE: KA = RoPE (k)())). We automatically choose the number of levels M from the total number of heads in the pretrained architecture:
Qa = RoPE(()((Q()))
M loga (3H 1) W
1
... + 4 which represents the total number of hierarchical heads that can be accommodated under the current architecture. Each head index h E {l...., H} maps directly to a level via the rule that exactly matches the geometric quotas 1:4: whose total sums W, and falls back the original RoPE = 0) for surplus heads:
where W is the cumulative geometric series + 4 +...
loga (3h (3h + 11] 1, h W, [ 0,
4. =
clipped to [0, M 1].
h > W
Any heads beyond the geometric budget W default to / = 0 to minimize disruption of pretrained patch-level priors. Taking Flux as an example, we divide each sub-vector into three levels: Flux, there are 24 heads in total. The first head corresponds to 1 = 0, i.e., the original patch-level RoPE. Heads 2-5 are assigned 1 and heads 6-21 to 2. The remaining heads 22 22-24 cannot be allocated under this scheme and are therefore reassigned back to / = O. As illustrated in Figure different colors indicate different PE levels. The coarsest level corresponds to a 16 16-pixel patch, while the finest level corresponds to 4 4-pixel patch. This hierarchical design enables flexible spatial transformations: direct manipulations of sub-patch RoPE yield local geometric adjustments in the reconstruction while preserving pretrained patch-level correspondences.
3.3 DEPTH-AWARE ROTARY POSITIONAL ENCODING
In standard 2D RoPE, the horizontal (z) and vertical (y) coordinates are encoded independently. Each axis is assigned a dedicated subspace the embedding vector, within which a ID RoPE is applied. Concretely, the token vector is partitioned into two segments, one modulated by the RoPE corresponding to the horizontal coordinate x and the other by the RoPE for the vertical coordinate y. This factorized scheme ensures that the dot product of two rotated queries and keys encodes relative displacements along both axes, while keeping the rotations invertible and dimensionally consistent.
To allow DIT to leverage positional encodings for reasoning about depth relationships between kens that overlap in the 2D projection, following the above principle, we extend RoPE to include a third spatial axis for depth, which refers to the distance each pixel's corresponding 3D point from the camera along the optical axis (that is, its z coordinate in the camera coordinate system). In addition to the subspaces for (x, y), we introduce another subspace for the depth z. Each coordinate (ar y. 2) thus has its own ID RoPE encoding, applied to a disjoint part of the embedding vector:
Q (h) = RoPE!!.) (1)),, RoPE (Q()), RoPE!")(Q!!) ]. K (h) (ROPE())) (w) (K)())))())))) RoPE( (K()), RoPE (K!*)]
where Q! (1) to each axis. This extension yields 3D spatial RoPE that encodes relative offsets not only in the image plane but also along the depth axis, enabling the Transformer to model volumetric correspon- dences and maintain geometric consistency across viewpoints.
Q (h) (and K
denote the corresponding vector segments allocated
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Replenish
DiT
Gaussian Noise
XT
Target View Result Xtge
Warping PE
Conditional Source View Karc
Discard
Rocontruction & Change View
Figure 4: The transformer takes both noise tokens and source-view image tokens. Noise tokens are placed on 2D grid with depth set to zero, while image tokens are assigned hierarchical PEs according to their projected positions from monocular reconstruction and view transformation, with depth values taken from the reconstruction. Tokens projected outside the grid (e.g., index 6) are discarded, and empty grid locations without image tokens (e.g., index 0) are filled by noise, which is refined to generate plausible content.
3.4 OVERALL ARCHITECTURE AND TRAINING OBJECTIVE
These two components together form new 3D field-based positional encoding, which we apply to the DiT architecture to jointly process noise tokens and source-view image tokens, resulting in NVS-DiT model. As illustrated in Figure noise tokens are placed regular 2D grid with depth initialized to zero, while source-view image tokens are projected into the target camera view via monocular reconstruction and view transformation. Each image token is assigned hierarchical 3D positional encoding (æ, y, z) that captures its detailed target spatial location and depth. Tokens discarded, and empty positions are filled with noise tokens,
projected outside the valid grid which are progressively refined by the transformer to generate geometrically consistent content. This design enables the model to integrate observed image evidence with generative completion, achieving novel view synthesis within the DiT framework.
To train the model, leverage multi-view supervision under a rectified-flow (Liu al. 2022 objective. Specifically, we adopt the rectified flow now-matching loss:
Co E Emp(()) Zege.aare frawa PE [100 (2,,, x (rans-PP)) (E Ftgt =1gg))1
where a ydrone-PE and Figt denote the image tokens of the source view with transformed PEs and serc the target view, respectively, obtained by the corresponding DiT's VAE encoder. 2 the linearly interpolated latent between clean latent Zzgt and Gaussian noise e NN 1), defined as 2 (1 t)Zggt + te.
EXPERIMENTS
4.1 IMPLEMENTATION DETAILS
Our model is built on Flux.1 Kontext (Labs et al., 2025), which generates images conditioned on text prompt and a reference image. This architecture naturally aligns with our design, as already integrates reference-image tokens, providing seamless foundation for incorporating our PE- FE-Field framework. We remove its text input and condition solely on the reference image. To train two multi-view datasets, DL3DV (Ling al. 2024) and MannequiCChal-
NVS model, lenge (Li et al.) (020)), both processed with VGGT (Wang et al.) (025) ) to obtain per-image depth maps and corresponding camera poses. Additional details provided in the Appendix.

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Published as a conference paper at ICLR 2026
Source view
Ours
Gen3C
NVS-Solver
ViewCrafter
GenWarp
Visualization of novel view synthesis results where the source image (left) is rotated 30 to the right. Compared with other methods, our approach achieves accurate viewpoint transformation while preserving consistency with the source image and avoiding noticeable artifacts.
Figure 5:
Input
Ours
FLUX.I Kontext
Qwen-Image-Edii
Figure 6: Comparison with prompt-based image editing methods. Our approach enables accurate control of rotation angles while maintaining consistency with the input image.
4.2 COMPARISONS WITH RELEVANT METHODS
We mainly compare our approach with several baseline methods (listed in Table 1 in the single- image novel view synthesis setting. Experiments are conducted on three datasets, Tanks-and- Temples (Knapitsch al. 2017). RE10K (Zhou et al. 2018), and DL3DV (Ling et al. 2024). In each case, a single input image is provided, and subsequent frames are generated under different target viewpoints. For methods that require depth point cloud conditional input, uniformly use the predictions obtained from VGGT as input, We then calculated three metrics, PSNR, SSIM (Wang al., 2004), and LPIPS (Zhang et al. 2018), and reported the average scores for all test samples in Table Our method outperforms existing approaches across all metrics on all three datasets. Qualitative comparison with subset of representative methods is presented in Figure 5 We observe that GEN3C often propagates reconstruction artifacts into the final results, leading to noticeable white streaks and irregular boundaries. NVS-Solver and ViewCrafie tend to introduce depth-warping errors, which negatively affect the geometric accuracy of the synthesized novel views. Gen Warp produces unsatisfactory results due to the absence of depth information its coordinate representation and the misalignment between its coordinate system and the input image. Due to space limitations, more qualitative comparisons are provided in the Appendix. is worth noting that, unlike many video-based models listed here, our approach does not require generating inter- mediate frames between viewpoints, making it over an order magnitude faster than video-based method to generate target view while still producing geometrically consistent results.

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Tanks-and-Temples
REIOK
DL3DV
Method
PSNR
SSIM
LPIPS
PSNR1
SSIM
LPIPS}
PSNR1
SSIMI
LPIPS
ZeroNVS Sargent al.
2024
13.14
0.327
0.516
15.23
0.540
0.386
14.17
0.441
0.481
CameraCtri (Hc 2024
15.34
0.534
0.331
17.74
0.681
0.278
16.31
0.552
0.352
GenWarp Sco et al. 2024
16,45
0.513
0.377
15.30
0.538
0.371
13.81
0.531
0.382
NVS-Solver You al 2024)
16.73
0.521
0.323
17.00
0.673
0.314
16.86
0.543
0.341
ViewCrafter Yuu ct al 2024)
17.18
0.589
0.346
17.75
0.681
0.315
17.24
0.571
0.329
DimensionX (Sun et 20244
17.78
0.635
0.228
18.21
0.717
0.307
18.22
0.653
0.201
SEVA 7hoou al.
20:25
17.61
0.621
0.235
17.58
0.688
0.334
18.01
0.638
0.214
MVGenMaster (Cao ct
202.
18.03
0.622
0.253
17.87
0.701
0.321
17.71
0.586
0.277
See3D (Ma et al. 2025
18.35
0.641
0.244
18.24
0.735
0.293
18.41
0.631
0.215
Voyager (Tuang ei al.
2025
18.61
0,669
0.238
18.56
0.723
0.264
18.84
0.636
0.227
Forl CCen
2025
18.91
0.675
0.236
18.03
0.691
0.282
18.67
0.645
0.218
GEN3C Ren
19.18
0.681
0.207
20.64
0.754
0.229
19.14
0.658
0.198
Original PE
20.03
0.683
0.221
20.17
0.752
0.233
19.92
0.667
0.201
w/o Depth
20.63
0.692
0.217
20.33
0.767
0.227
20.46
0.695
0.194
w/o Multi-Level
21.97
0.718
0.180
21.42
0.809
0.168
21.91
0.733
0.162
Ours
22.12
0.732
0.174
21.65
0.816
0.162
22.23
0.742
0.154
Table 1: Quantitative comparison of different methods on Tanks-and -empslees,s REIOK, and DL3DV datasets. We report the average PSNR, SSIM, and L.PPSS scores novel view synthesis from single input image.
Beyond pose-conditioned approaches, recent image editing models such as Flux.1 Kontext (Labs et al. 2025) and Owen-Image-Fode (Wu et al.) (2025) also demonstrate strong capabilities in view- point manipulation. We further compare our method with these prompt-based editing results, as il- lustrated in Figureló) Flux is generally insensitive to prompts specifying spatial viewpoint changes, often producing only minor viewpoint variations while introducing noticeable artifacts. Qwen, on the other hand, achieves more pronounced spatial editing effects than Flux, but tends alter the original image tokens. As shown in the rightmost example of Figure 6 the result appears overly smoothed and even alters the person's 's identity. Overall, it remains very challenging precisely control viewpoint changes through prompts. More comparisons can be found in the Appendix.
Input
Warped Image
wio Multi-level
Original
Input
Warped Image
w/o Depth
Original PE
Ours
Figure 7: Ablation studies. Removing the detailed positional encoding or depth leads to different
types of degradation in the generated results.
4.3 ABLATION STUDIES
We mainly analyze the effect of removing our two key components: the hierarchical detailed po- sitional encodings and the additional depth-awart extension. The quantitative impact of removing each component can be observed in Table [ while Figure provides two illustrative cases. As shown in the top example of Figure 7 when the multi-level positional encoding (particularly the detailed level) is removed, undesirable distortions appear due to the mismatch between patch-level positional encodings and the reconstruction. When depth information is removed (see bottom ex- ample in Figure the generated images suffer from severe spatial misalignment.
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Source view
Step
Step 2
Step 5
Direct
Figure 8: Multi-step generation. Left: input image. Top: generated results. Bottom: rotated point clouds. Right: direct one-step generation.
aftela
2 AGRVNC
R AGENST SO
Input
Transformation
Result
Input
Removing
Result
Figure 9: Applications. The left example shows object 3D editing, while the right example shows object removal, highlighting the versatility our model in different spatial editing tasks.
When applying our method to generate results under large viewpoint changes, the model is required directly generate a substantial amount of unseen content, which increases the generation burden and may compromise consistency with the source image. To mitigate this issue, we decompose the transformation into multiple steps, in which the model only needs complete small portion of the missing content in each step. As shown in Figure X we divide the transformation of the target viewpoint into five steps. After each step, the newly generated content is fused back into the image tokens of the original viewpoint, and the fused tokens (or point cloud) are then transformed to the next intermediate viewpoint for subsequent generation. Compared to directly transforming to the target viewpoint in step (rightmost result in Figure R). this progressive strategy produces results that are more consistent with the source view. See Appendix for quantitative comparisons.
4.4 OTHER APPLICATIONS
After training, our NVS model acquires the ability to reason over visual tokens in 3D space and generate consistent content. Consequently, it can naturally adapt to other tasks with similar spatial logic, even in the absence of task-specific training. As illustrated in Figure in the left example we perform object-level 3D editing by isolating the point cloud of the book, rotating it to a new viewpoint, and recomposing with the original background. In the right example, removal by discarding the tokens corresponding to the masked human region and replenishing them with noise, resulting in realistic removal effect. More results be found in the Appendix.
achieve object

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5 CONCLUSIONS
In this work, we revisited the internal mechanisms of Diffusion Transformers and revealed that spatial coherence is largely governed by positional encodings rather than explicit token interactions. Building on this observation, we introduced the Positional Encoding Field (PE-Field)) which extends standard 2D encodings into a 3D, depth-aware and hierarchical framework. This design equips DiTs with geometry-aware generative capabilities, achieving state-of-the-art results on single-image novel view synthesis while also enabling flexible and controllable spatial image editing. We hope our study sheds light on the overlooked role of positional encodings and inspires future research into more principled and spatially grounded generative architectures.
Acknowledgements. This work was supported by NSF-2047677, NSF-2413161, NSF-2504906, NSF-2515626, and GIFTs from Adobe and Google. This work was supported by computing support on the Vista GPU Cluster through the Center for Generative AI (CGAI) and the Texas Advanced Computing Center (TACC) at UT Austin.
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13


Reviews:
[{"review_id": "CH5BfQECEX", "reviewer": "Reviewer_WUCM", "summary": "This paper builds upon a very interesting idea that DiT attention pattern is very very local. Starting from this idea, the authors gained the intution of editting the position/strcture/viewpoints of the image through editting the positional encoding of the DiT. The author conducted simple experiments in Figure-1 to show this concept. \n\n\n\nGiven these insights and polit study, the author developed more sophisticated designs for 3D-aware positional encodings. With this, the author builds upon flux-context (an open source image editting model) to implement his algorithm. The author finetuned the model on DL3DV MannequinChanllege with processed depth-map and camera poses.  After finetuning, the author showed impressive results with NVS on portaits images, object images and sceneray images.  Even though a simple call of the model can only generate relative view shifts, the author showed larger view-shift results by recurrsively applying the model.  When comparing with other methods, the author showed a higher PSNR.", "questions": "Is it possible to build a training free baseline using the warpped 2D RoPE?  Cause from the intuition of Figure-1, it seems possible to build a training free baseline?  Correct me if I am wrong.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. The idea is quite neat. With polit study to build up intuitions, and interesting designs, and also good experiment design to validate the idea\n2. The results are quite impressive! The visual quality is quite high. I do understand that each simple forward pass of the model can only edits a small view shifts. To address this, the author also showed recurssvely applied results, which is also quite cool. \n3. The overall presentation is quite clear, and I can easily follow the logics of the author.", "weaknesses": "I lean towards accept the paper. \n\nThere are only several minor points, I don't think these are real weakness. \n\n1. This methods is hard to be applied to multi-view novel view synthesis.  Maybe it's still possible is to build one single reference images by merging patches from multiple input views?  \n2. This demo would be even cooler if there are videos attached.  (Novel-view-synthesis videos with smoothly moving cameras.)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "gM61Og0nlF", "reviewer": "Reviewer_o2gX", "summary": "This paper presents a positional encoding field for novel view synthesis based on the DiT model. It is inspirted from the shuffling experiment and visualization of the position encoding for a standard model. The proposed method includes two parts: multi-level positional encodings for sub-patch detail modeling, and depth-aware extension to the rotary encoding. The proposed method has been evaluated on three datasets: Tanks-and-Temples, RE10K, and DL3DV. Both quantitative and qualitative experimental results demonstrate the effectiveness of the proposed method.", "questions": "Generally this is a good paper. However the fair comparison issue makes it difficult to identify the real improvement made by the proposed method since it is mixed together with the powerful Flux backbone. Please see the questions in the weaknesses part.", "limitations": "", "rating": 2, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1.[effectiveness] The proposed method consistently outperforms the previous methods both qualitatively and quantitatively.\n\n2.[motivation] The proposed method is well-motivated. It starts from an observation by shuffling the positional encodings. That helps the readers to better understand the motivation and design of the proposed method.\n\n3.[ablations] Ablation studies has been carried out to demonstrate the effectiveness of individual components in the proposed method in section 4.3\n\n4.[extension] The proposed method has probably more potential to be used in other spatial editing tasks as mentioned in section 4.4", "weaknesses": "1.[clarity] As described on L033-041, as well as figure 1, the proposed method is motivated by a position encoding shuffling experiment. What would be the worst case for a shuffled or re-ordered position encoding? How does that impact the model? If there is a threshold beyond which the generated output is completely messed up, the authors might have to rethink the connection between the position encoding shuffling expeirment and the proposed method.\n\n2.[typesetting] The macro \"\\citep\" or \"\\citet\" should be used instead of a plain \"\\cite\". The brackets are missing in manyplaces like the related works section, which makes it not easy to read.\n\n3.[clarity] The caption of figure 1 is confusing. What does \"perturbed\" mean? The paper and the figure says \"warp, shuffle, reorder\". What is re-order again? Are they the same thing? Please use a consistent term to avoid confusion.\n\n4.[clarity] On line 145, how are they re-ordered? Is it random?\n\n5.[clarity] On line 246: how is the depth obtained during the training and testing process of the proposed method?\n\n6.[design] The proposed method is only tested on the Flux model. Does it apply to other DiT-based models, such as the MMDiT (stable diffusion 3)? If so, the proposed method would be helpful for a wider community.\n\n7.[fair comparison] In table 1, the proposed method outperforms the previous methods. But not every other method is built-on the Flux model. Therefore, it is unknown how much performance improvement originates from the Flux backbone itself. This would raise a fair comparison issue, and leave the real improvement of the proposed method in question.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3uV0yZcLIW", "reviewer": "Reviewer_NKTZ", "summary": "In this paper, the authors find that global spatial coherence comes from positional encodings (PEs) rather than token–token coupling, in which perturbing PEs preserves semantics while reorganizing layout. Based on this insight, the authors investigate the effect of PEs in the image generation process. And a new and neat positional encoding method is proposed that combines a 3D encoding (additional depth information) and a fine-grained patch encoding. With the proposed positional encoding manner, the PE-Field–augmented DiT achieves state-of-the-art performance on single-image novel view synthesis.", "questions": "1. Does the text-editing prompt influence the 3D-Positional encoding for view synthesis based on Flux Kontext? \n\n2. Additionally, what is the instinct difference for text-control and PEs-control for view synthesis (visual editing and generation) during the training process?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Interesting Concept Finding. The authors find that PEs control the spatial structure coherence during image generating or reconstructing process, motivating a new potential way for visual editing or synthesis.\n\n2. Novel and Effective Positional Encoding. The authors consider the depth-aware information and more fine-grained semantics in the patch, then propose a new positional encoding that locates both the mentioned information.\n\n3. Good Synthesis Result. With the proposed positional encoding, the introduced PE-augmented DiT achieves SOTA performance on single-image novel view synthesis.", "weaknesses": "1. Over-dependence on Monocular Reconstruction. As shown in the main framework, the monocular reconstruction provides essential 3D positional information for new view generation. How about the model’s robustness to terrible or noisy 3D position info injection?  \n\n2. Concerns about Multi-Level Positional Encoding. The head-layer match in fine-grained positional encoding is handcrafted in order.  More matching ways should be conducted to verify its robustness for fine-grained positional encoding.\n\n3. More View Generation Scenes Discussion. 1) The visualization result from unseen view to seen view (i.e., view from left face to front face) should be reported. 2) Object-level or Region-level view synthesis. \n\n4. Computing Cost Discussion. Since the proposed framework relies on monocular reconstruction, it may incur additional cost.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)